Sounds like a fun party! You absolutely don't need to worry about siblings or adults. The invitation will be made out to the child, and that is who you would pay for. By age 5, most parents probably assume they are dropping their child off for the party and picking up after. If they feel like they want to stay to keep an eye on their kid (being overprotective myself I might have hung around just to keep myself from going crazy) they will probably let you know that they would like to stay. I would be surprised and offended if they strapped on a pair of bowling shoes and started eating on your dime. Really not likely. If someone does want to stay and you're worried about the money, just pre-emptively say something like "that's great, we'll see you there- and you can probably get a cheaper rate if you pay with our party if you are wanting to bowl". Something that says you're fine if they stay, but clearly avoiding any money issues.
Again, I really wouldn't worry. Most will probably just drop off and pick up. You are not being rude and cheap at all. I have never heard of anyone trying to bring themselves and siblings and expect the host to pay.