There are a couple of things from a legal standpoint...
1) Standard of assumed risk. If we have a lawyer here, he can tell you what the acceptable level of assumed risk is in bowling, but it's a part of all sports-related injuries and claims and sliding while wearing shoes already puts you under some level of assumed risk.
2) If the total amount of your injuries ends up being a key bruise and some bruised pride, you have no real loss, therefore no claim.
On a side note, I was commiserating right along with you until you got to the part about suing. Please, we have enough lawsuit abuse in this country as is. We've all fallen in a bowling alley before. Complain to the management and leave it at that.
Jess