In Bleeding Edge you are not stuck with the character you chose to enter a fight with, and you should change your character to counter your opponents. So, how do you change character?
You can change character at any point in a match from the respawn area.
In order to change your character mid-match you first need to be in the respawn area. You can get there by either running back to it, or via death. Whether physically within a respawn area or waiting to return to the fight you can change character by pressing H or Up on the D-Pad. From here you will have the character select screen appear, and you will choose your new fighter and one of their two supers (you can also use this technique to swap supers if you have no desire to alter who you are playing).
There is a limitation to swapping your character: no duplicates allowed. This means you can’t field a team full of ZeroCools or Maeves, so whoever you want to play as needs to be out of action. If you want to play as someone a fellow teammate is currently controlling you will have to ask them to relinquish that character. Otherwise, you will not be able to choose that character.