Rogue has several stats combination Event : Slip Away, Cheap Shot, Breaking and Entering. This is similar to Slip Away except with different stats pair. That's welcomed because now either intellect-leaning or combat-leaning Rogue can get a high accuracy Evade, which is helpful in high player count boss fights or enemies laden with keywords and while-ready effects.

However note that Bum's Rush has 3 effects : exhaust, bonus damage (over success), and push. Slip Away has just 2 effects : exhaust, and long evade (over success). I think in many dicey situations, the "push" in Bum's Rush and "long evade" in Slip Away is the desirable outcome so you don't have to deal with it again too soon. Though both doesn't work with Elite, Bum's Rush "push" is not gated by over-success like Slip Away "long evade", so the spent 2 resources for Bum's Rush is more likely to work without additional commits. You can also push non-Hunter away and stop worrying about it. 1 damage is a nice bonus, and if that brings HP down to nice number and you intended to finish it, you can decide not to push with the "may" clause.

However if you decided to push and they have Hunter, they do get priority attack if they just move in and hit you the next round, unless you move further away or move into it.

Based on the wording of other cards with multiple conditionals, eg Rite of Seeking, the push on Bum Rush appears to be unrelated to if you succeeded the evasion attempt.

That would mean Bum Rush can be used to "permanently" deal with non-hunter non-elite enemies, preferably also non-alert.