Invite them first!
It's easy. Your town probably has one or more of the following:
* bowling alley
* movie theatre
* mini golf course
* fast food restaurant
etc. etc. you get the idea. Places that are not too expensive and are very safe and people have interest in them.
Then just tell your pals something like, "I'm going to the movies this weekend at the Octiplex, probably around 8 o'clock. Not sure what I want to see. Wanna come along and we can all go to something?"
That way it's very noncomittal. They can come or not, say yes or no, and it's not fraught with a huge amount of meaning but it can entice them out. Yes, you don't have good transportation options, but surely you can either walk or ask a friend or family member to drive you? Or make it an afternoon thing, and then walk both ways if the distance is reasonable.
The old saying is, to have a friend, be a friend
. So if you want to be invited to things, you're probably going to have to make the first move. But once the first move is made, other things will fall into place.