What would I do?? I would not have a bowling party b/c I don;t have the money..
Now that op is in this spot, I would just call the mom and start out with "I can't pick up b/c I don;t have room" and see what she says. And if she says that is ok then she can't come, not a prob. but if she says that she can take her I would just tell her the truth and how much it would cost if she went and see what mom says. mom will most likely say no b/c of the money. I don;t think this is a big deal nor should it be made into a big a deal. as far as calling the mom before hand, how do we know she has her #??? I do know that when my kids were younger and having their parties I did NOT have the #s to any of their friends at school.

Now that op is in this spot, I would just call the mom and start out with "I can't pick up b/c I don;t have room" and see what she says. And if she says that is ok then she can't come, not a prob. but if she says that she can take her I would just tell her the truth and how much it would cost if she went and see what mom says. mom will most likely say no b/c of the money. I don;t think this is a big deal nor should it be made into a big a deal. as far as calling the mom before hand, how do we know she has her #??? I do know that when my kids were younger and having their parties I did NOT have the #s to any of their friends at school.
We invite the kids we want to be there in the first place!
That's what got OP into this mess in the first place.

We stopped doing those type of parties, and that's one of the reasons. We did the inflatable/gymnastic/kids museum (and more I can't think of) when they were very young. Now we do something special with just the family, the birthday child gets to pick, and they are happy. I know I'm happy!
The reason you have an RSVP date is so that you can give a headcount to the establishment and get all the stuff you need to in order (goodie bags, ballonon, etc) in advance of the party. RSVPing late is rude and inconsiderate, and asking the party mom to drive your kid is beyond rude because that mom obviously didn't think that it mattered.