。
If they're busy, I don't want to bother them.
Literal
Busy doing-if their disturbance [object-を] want-to-do [contrastive-は] not.
忙しくしている means 'is keeping busy' — する adds intentionality to the adjective. なら is a conditional ('if that's the case'). 邪魔をする (to disturb) is a common set phrase. ~たくはない inserts は into the negative desire form for contrastive emphasis — 'as for wanting to, I don't.' The は carves out the speaker's reluctance as the focus.