The less you say, the better. You say, "Thank you for the invitation, but Petunia will not be able to come." If you really want to add detail, you can say that she has plans the next morning so she can't do the sleepover. (Now, those plans can be "sleep late and watch cartoons" but you don't say that. Same as when we were teens, declining a date was "So sorry, I have plans" even if those plans were to wash our hair.) You can either suggest that she do the bowling/dinner part and you'll pick her up, or you can wait for the other parent to offer that. Be careful because it might sound like your daughter only wants to do the fun stuff and wants to pick/choose.
You open yourself up to questions, though, the more you say. So you have to have a secondary response if the parents ask why no sleepover. This will come up more for 2nd and 3rd invitations. "Just not her thing," is an acceptable response but can involve some grilling. And your child needs to be prepared that kids will ask her why she isn't coming. If she says, "My parents don't allow it" or "My parents don't agree with parenting styles," then you put her on the front lines of appearing to insult the other parents. So don't put her in that position. If she wants to say, "I just like my own bed," fine. But kids may think she's afraid so she needs to be taught your values and that the less said, the better. This will increase over the next few years of middle school and high school, so best to get your ducks in a row now.