In Sorry, when using the 7 split card, am I allowed to split the 7 to bump an opponents pawn to home and finish the count with another pawn of mine. It doesn't really specify in rules of the 7 split but I am allowed to bump opponent if I land on their spot in bump rules. Please clarify.
Yes, you can split the seven between two pawns. If one of the pawns ends on a space occupied by another player's pawn, that other pawn is sent back to Start (not Home).
The only restrictions noted for the split are that you must use all of the 7, and you cannot start your own pawn.
7 - Moves one pawn forward 7 spaces or can split the forward move between any two pawns. Using this card to start a pawn is against the Sorry rules. The instructions do state that you can part of the 7 to get a pawn Home but that you must be able to use the balance of the move for another pawn.
If you mean "split" the seven into two moves with a single pawn, then no. That's not splitting the seven. (again by the quoted rules)