Is rolling to escape a monster required?
No you can't choose to take the Bad Stuff, you must always attempt to Run Away first.

From the Munchkin rules (page 3 under Combat):


  If the monster’s combat strength is equal to yours,
  or greater, you lose the combat and must Run Away


Also from page 5 under Running Away:


  If nobody will help you . . . or if somebody tries to help, and your fellow
  party members interfere so the two of you still cannot win . . . you must Run
  Away.


Note that in both cases they use the word must - you do not have the choice to run away (or not) - you must make the Run Away check, and must include all bonuses from active Races/Classes etc.

However you could still play one shot cards against yourself to change the possible outcome eg. a loaded die to change the die result to a 1, or a lose your class card to remove a class that gives you a bonus to running away.