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.
Ring of Spell Storing
Have the NPC use a Ring of Spell Storing, a "standard" magic item. It can store up to 5 levels of spell. Some other relevant features for the item:
Any creature can Cast a Spell of 1st through 5th Level into the ring by touching the ring as the spell is cast. The spell has no Effect, other than to be stored in the ring.
While wearing this ring, you can cast any spell stored in it. The spell uses the slot level, spell save DC, spell Attack bonus, and Spellcasting Ability of the original caster, but is otherwise treated as if you cast the spell. The spell cast from the ring is no longer stored in it, freeing up space.
So the NPC could have found such a ring with a single Sending in it at some point. They had it identified, and now's time to use that Sending. No wizard needed at this time.
The NPC could also have had the ring for a long time already (as a family heirloom maybe), and they just need to free 3 levels worth of room from the ring, and find a Wizard to cast a single sending to the ring. Or maybe even in this case the ring has Sending already, as it seems a very logical thing to put into a ring, for emergency use.
Best Answer
NPC's are not restricted to the same spells the players use.
You can just say the NPC's version of teleport allow them to exclude themselves. Chapter 10, Spellcasting, points out that there are far, far more spells than those listed in the existing books.
NPC's are not restricted to the same spells as players; spells for players are created for balance and playability. It is entirely possible, if not expected, that an NPC might know a spell they players don't or has a different version of the spell. Page 283 in the DMG has guidelines for creating new spells.
If you need the NPC to be able to teleport the players, they can. Whether it is by spell, boon, scroll, magic item, or a ritual requiring twelve apprentice mages and the alignment of the stars. You as the DM define the world.
You can make it subtle or obvious. From "Bob points a stick at you says a single word and you disappear" to "Bob the wizard and 5 of his apprentices form a circle around you and begin chanting for ten minutes" If your players try to identify the spell and succeed at their arcana check, you can say "Bob the wizard appears to be using a variant of the teleport spell"
If you're worried about balance, put restrictions on it. Maybe the spell only works from a permanent glyph the NPC has spent months making (A reverse circle of teleportation so to speak). Maybe it requires 6 other people with spellcasting abilities and takes ten minutes to cast. Maybe it requires rare, hard-to-find material components that are consumed. Maybe it does not actually teleport them but fires them into the sky in a ball of energy that streaks to the target location in a matter of hours. You can even have fun with this by having the spell dump them high in the air and they then have to expend spells or resources to make it to the ground safely. You can even scare the players with Bob the wizard saying prior to launch: "Be careful I haven't worked out all the bugs in this spell yet, landing can be a little wiggy".