There are no rules in D&D 5e that cover this.

Or to more explicit, there are overland travel rules, and there is nothing in them that change the pace at which you can travel overland based on your ability to move extra distance by taking a bonus action.

There is very little in the way of precedent however. Rogues can take a bonus action in combat to dash; this explicitly doesn't let them do it out of combat. Using your Action to Dash is presumably factored into overland movement (or trying harder and going faster).

So this ends up being left to the DM.

Why this ability to step as a bonus action might not make you move faster is that using magic might be distracting and tiring, much like using your action to dash is tiring. On the scale of combat, it isn't important (combat is presumed to be an intensive activity that wears you out), but in overland travel it might end up costing you more endurance than it gains you in speed.

On the other hand, even if it is effortful, common sense says that being able to teleport 30' in a fraction of a second every 6 seconds is going to make at least some travel much easier.

In terrain that isn't a completely flat, well maintained road, being able to "step" over stuff that might slow you down (a section of road with potholes, a stream, up a hill that would otherwise require climbing or a detour, past some brambles, etc) would speed you up.

Finally, there is the rule of cool. This character is an 18th level wizard who can teleport whenever she wants to. Being able to use this to increase your overland movement speed is both cool and creative. There isn't precedent that I am aware of that it shouldn't work, there is no huge balance impact on a wizard moving overland faster, and such an ability is well below the power scale of 18th level characters.

I'd say go for it. Maybe don't double travel speed, but grant the wizard +50% in the best situation (high quality roads), and halve the penalty of rough terrain (compared to the best situation) for the wizard.

A mundane mount would not be teleported with you

Misty step has a range of self which means it affects only the caster.

Briefly surrounded by silvery mist, you teleport up to 30 feet to an unoccupied space that you can see.

It also has no text allowing for additional creatures to come along with you. The caster and the horse are separate creatures. Thus, the horse would not get affected by the spell.

Compare this to dimension door which says:

You can also bring one willing creature of your size or smaller [...]

Dimension door allows you to bring other creatures, but misty step does not have the same or similar text so it does not. (Side note: dimension door would also not work on teleporting a steed because it is bigger than you.)

If your mount is from find steed or find greater steed, then it will be teleported as well

If your steed was summoned using find steed or find greater steed, then misty step would affect them because the spell specifically says:

While mounted on [your summoned mount], you can make any spell that targets only you also target the mount.

Of course again this is only specific to steeds created by these two spells.