This is a difficult situation. I've babysat many children before and once or twice the parents have asked me to stay with them or even lie down with them until they go to sleep. I sometimes sit on the bed next to them while reading their bedtime story but after that I might sit next to the bed until they goto sleep before slipping away. More commonly the children (or child) asks you to stay with them until they sleep.
I don't really find anything wrong with it or have a problem with it. But I'm always very concious of what happened to Michael Jackson and so sometime feel uncomfortable when I do it so I'm very careful how I behave and what I say to the children and around it. Thankfully, all of the parents I work with are quite laid back about it as they trust me to handle it appropriately. But if it was with a family I didn't know well it would be a different story.
I don't believe you are a pervert but I would discourage the children from sharing your bed, especially the 11-year-old, and do something similar to what I do. And unfortunately, if you're a guy (though I'm guessing you're not - Demonic Vixen), sleeping with a young girl is definately a big no-no unless it's your own child.
Sitting with them untill they go to sleep is one thing but staying and sharing a bed is another. I know the children and their parents trust you but I understand completely that the neighbour finds the concept inappropriate and she proberbly won't be alone.
I would avoid it if for no other reason that if the children say something completely innocent that can be taken the wrong way and that can quickly destroy the parents trust and get you in trouble with the police. Or at the very least destroy your reputation as a good babysitter.
It doesn't take much, you are treading an awfully fine line. I'd get out of the children's beds (or get them out of yours, whichever way it is) or avoid babysitting for them in the future ... honestly from one babysitter to another.