I've played the "normal" version of Killer Bunnies Quest (i.e. Blue and Yellow decks) and also the Remix version. I found the normal version can be a bit slow mainly due to a lack of Bunnies - there are 25 Bunnies out of about 160 cards so if you don't have a Bunny you can be waiting a long time to pick one up.
For the normal version I'm planning on trying the following rules:
Everyone Starts With A Bunny
Anyone who wasn't dealt a Bunny at the start can go through the draw deck until they find a Bunny and discard one of the cards they were dealt.
This is suggested in the rules for the first time you play, but I see no reason not to do it every time.
You Can Buy Dead Bunnies
When Bunnies die put them in a separate pile. Dead Bunny cards can be bought for 10 dolla. The Bunny card is placed in your hand and has to put through the run as normal.
This rule is in the Remix version (and I think it's in one of the later expansion decks too), it seems to speed things up considerably.
Give everyone some tokens (I'm going to use Monopoly money) at the start that represent dolla, these tokens act exactly the same as normal money. I'm going to try giving everyone 10 dolla, that's enough to buy a Bunny or a Carrot and it's usually enough to feed a Bunny.
A slight variation on this would be for everyone to get some free money at the start of their go instead, I'd suggest 1 or 2 dolla.