Taken from the Player's Handbook (p. 74)
Maneuvering Attack. When you hit a creature with a weapon attack, you can expend one superiority die to maneuver one of your comrades into a more advantageous position. You add the superiority die to the attack’s damage roll, and you choose a friendly creature who can see or hear you. That creature can use its reaction to move up to half its speed without provoking opportunity attacks from the target of your attack.
Can the "friendly creature who can see or hear you" be the Battle Master who is spending the superiority die / making the attack?
This is how this type of phrasing is applied to spells, and a reaction can occur on your turn or someone else's, so the way the maneuver is worded makes this a viable idea in my mind.
However, is hitting with an attack, then leaving without taking an opp. attack, and being able to move 45 feet overpowered?
The answer to the question makes or breaks the usefulness of this maneuver.
What if the Battle Master were the only character in the party? (solo adventurer)