It sounds like your fellow roleplayer just wants you to be verbally clear about what exactly you're doing mechanically without just pointing to a thing on your character sheet. It doesn't sound like their problem is that you're roleplaying at all—I'd be pretty surprised if they disliked flavourful descriptions of how people do things.
It's pretty easy to verbally express what you're doing mechanically and what you're doing flavourfully side by side. Doing one doesn't preclude doing the other. You could say something like this:
I walk up to the dog, and I'm going to use bardic music to fascinate it. I say good dog, good dog... as a repeating mantra.
Then your DM knows what's going on both in terms of mechanics and roleplay, and your fellow player does too, and nobody has to squint at your character sheet or have it held up to them whenever you do something for them to know what's going on.
Repeating “bard” again and again would be against roleplaying.
This isn't “against roleplaying.” It's just good communication. I roleplay regularly in my own games—I just say what I'm doing mechanically at the same time. Let's not misrepresent what will be happening: you're not going to be repeating “bard” again and again, you'll just be stating “bardic music” when that's what you're using. If the name bothers you then you could rename it to something you find more satisfying, like Fascinating Voice.
Maybe your specific brand of roleplaying involves avoiding any verbal mechanical description, but you should understand that's going to make things difficult and frustrating for some people.
Think of it this way: people are pretty bad at focusing on multiple things at once. Your fellow players can either focus on listening to you and watching you, or they can focus on looking at your character sheet and trying to read what you're pointing at, but they can't do both very well. Ever been to a talk where the presenter had a dozen bullet points on their slide, and if you tried to read them you'd realise you weren't absorbing what the presenter was saying? It's going to be like that.
So really, verbally stating what you're mechanically doing allows your players to focus entirely on watching and listening to you, meaning they can follow everything you're doing easily. That supports roleplaying and makes it easier for you and everyone else. Not doing this is more likely “against roleplaying” since it makes it harder for people to understand you.
You could talk with them and find out what will help accommodate them, but really I suggest you just accommodate your fellow player and take this as a lesson on communication.
Someone has to take the player who invited his girlfriend aside and talk to him one-on-one. (I'll address that to "you", for the moment, since I hope you'll get your GM to read this.)
Make it clear that it was OK to bring her, but not OK to turn game sessions into makeout sessions. Then lay down the unfortunate reality of the situation: if they can't cut it out, then one or both of them will be firmly uninvited, and soon.
When you do this, take care to not shame them for the makeouts (there's enough shaming around this stuff in life; no need to add to it), emphasising instead that it's just a poor choice of circumstances. Focus on how disruptive it is to the game people came for, and if you mention how it makes the group uncomfortable, soften that by emphasising that there's nothing wrong with a makeout itself — just the choice of time and place. Even better, congratulate them for their obvious happiness while asking them to save it for later or take it elsewhere.
There's a consent line they're crossing here too: by joining an intimate gathering and making out during it, they're making you all surprise visual and audio participants in this overtly sexual activity. That's super not cool, and not something anyone is obligated to be okay with. Again, not something to shame them for—the point here is that being not OK with this at the table is totally justified.
When you're not the GM or venue host, your option is slightly different: go to the GM, and have them do the one-on-one conversation and ultimatum instead.
If they won't, then you present them with your own unfortunate reality: this is not OK, and you will not be coming to the game anymore if the GM/host is unwilling to enforce reasonable social boundaries during their game / in their home.
Leaving sucks, but if the GM/host is going to abdicate their responsibility to make game sessions safe social spaces, then your most powerful tool for creating change is to enforce your own side of the social contract and exercise your right to leave. Chances are that if you have to go to that degree of effort, suddenly the GM/host will realise that they have imminent group destruction on their hands and will do the reasonable, pro-social thing of dealing with the offending people. (And if they won't, you've dodged a really nasty bullet!)
The alternative — staying anyway and hoping it will just get better — will most likely result in the group dissolving anyway. Either the players cut it out, or other players will start leaving after they become too uncomfortable. The sooner you present the ultimatum of "fix it or I walk", the more likely there will still be a group to fix when you give the ultimatum.
Oh, and as an illustrative aside: I have been that player who brought his girlfriend, and was stupid about overt makeouts. That group dissolved shortly after, and though we were all friends we soon drifted apart. Let my experience be your cautionary tale!
Best Answer
Since you stated 'parts of the group are very heavy on roleplay,' I'm assuming you are not the sole dissenter of the group. If you are, some of the options below won't apply.
Try the irrelevant roleplaying
Give it a shot. While it may not necessarily be your cup of tea, you may find yourself enjoying it more than you might think. Sometimes, random and perhaps somewhat pointless roleplaying in character can be an enjoyable process.
Talk to other players
With 3-4 players involved in the heavy roleplay that is not relevant to the campaign, the other players in the group should also share similar feelings as you do. Are the irrelevant roleplayers hogging the DM's time and giving them no chance to shine?
Ask them if they are happy with the current situation. If they are not, then you can approach the next step with better hopes for a successful outcome.
Talk to your DM
Like all problems in a campaign, you should discuss this with your DM. Your DM is the one running the campaign. Is he happy with the progress of the party? Or is he more concerned about how the heavy roleplay is stalling the campaign?
If he is happy, then you can only suggest that you and perhaps other players would like to see the campaign progress faster. Perhaps he can integrate the non-relevant roleplay and make it relevant somehow. For example, a character romance could be interrupted by a rich and mysterious playboy/girl who is secretly the villain boss/henchperson aiming to disrupt party cohesion so their schemes succeed.
Alternately, you could ask to do other things while the roleplayers are having their fun. Are they carousing with the barmaids and innkeeper? How about checking out the kitchen or innkeeper's room? Or perhaps the innkeep's son or daughter has a quest for you? Do other solo actions. This isn't the best option, but it may be the only one available.
If the DM is not happy, then you have the strongest ally on your side. Suggest ways to progress the campaign to areas with less irrelevant roleplay, like dungeons. Yes, character romances can continue here, but when trolls attack for the fifth time while the party bard is serenading their love, it will probably send the right message: the party is in a dangerous area - focus or die.
Are you having fun?
At the end of the day, we spend hours on this game to have fun. If you aren't, then try the above to ensure you are. If that still doesn't work, then yes, you should consider leaving the group.
This should only be the case when the DM is content with the situation, the other players are enjoying their time or not keen to rock the boat, and you find yourself feeling unhappy and unable to do anything about it. Otherwise, talking is your best option.