You were quoted the rules incorrectly.

First, Eldritch Blast has a casting time of 1 action (PHB p.237). You've only got one action on your turn, so you can only cast Eldritch Blast once. ("Off the shelf," that is. There are features, like the Sorceror's Quickened Spell, Action Surge, or even time stop that might change this.)

Boom. That's it. They can't cast a second eldritch blast as a bonus action, because the casting time of eldritch blast isn't "1 bonus action." (Compare with, say, healing word.)

But that's understandable.

It is possible for a caster to cast a spell as a bonus action and another as an action in one turn; the conditions are described exactly on PHB p.202:

• one spell has casting time of 1 bonus action,
• you've not used a bonus action for anything else this turn (because you can only take one bonus action per turn),
• the other spell is a cantrip,
• the other spell has a casting time of 1 action.

D&D is a great game in many ways. It has never, in my experience, been presented in its published materials in a way that makes sense to someone who doesn't already know the game. One player misunderstood something, and no other players nor the GM knew the rule well enough to course-correct mid-session.

That's fine. You now know. Alert your group as soon as possible and be ready for a group conversation about whether this should now be a table-rule, or will this just have been one shining moment in 'Lock's career. "Hey, guys, remember that one day when I was in beast-mode? My patron must have been having me on!"

The pushback lasts 1 minute or until your concentration is broken

The rules

A line of strong wind... blasts from you in a direction you choose for the spell’s duration.

When it says that the wind is blowing for the spell's duration it means that the wind is blowing for 1 minute (or until you stop concentrating on it).

The next line says:

Each creature that starts its turn in the line must succeed on a Strength saving throw or be pushed 15 feet away from you in a direction following the line.

So the line of wind is present for up to one minute, and, as long as that line is present, creatures that start their turn in it must save against its effect or be pushed back. The applies to every turn that a creature starts its turn in it for the record.

I'm afraid your DM is not following the rules as written. I think it is pretty clear that the spell works, and is intended to work, as I have described above.

Common sense

The fact that this is a concentration spell should be a giveaway that some continuing effect should be present. If not, what reason would there be to concentrate on it? What lasting benefit does it provide if not the titular wind?

Does it makes sense to have "strong wind" constantly blowing against people and not have them make saves or have any effect at all? It really doesn't.

Talking to your DM

Whatever you do, you must respect the DM's right and ability to modify the campaign as they see fit. However, you should bring up to them (privately if at all possible) and respectfully ask them to look it over again and see if they might have misread or misunderstood the spell.

If they are still insistent in the previous interpretation, explain to them how badly this nerfs the spell (especially compared to other 2nd level spells). Ask them if they would mind interpreting it your way for a session or two and see if they think it is overpowered (because it is not) or anything wrong becomes apparent to them.

If none of the above works, you may just have to live with it and might consider just not preparing it again if you think it is not worth it. You may also want to ask the DM if you should expect any other changes to rules/spells/abilities to head off any future misunderstandings (thanks @MC).

If there are other serious issues that are seriously affecting your enjoyment of the game you may want to consider starting to look for another group. However, do remember that this is only one spell and probably not worth ruining an otherwise stellar gaming experience for.