I've gotten a strap that goes over a conventional water bottle and hangs off a lanyard from the dollar store.
I also have one where it's a little sleeve to pop the bottle into. That one was a free giveaway. look in the camping section of stores/dollar stores
I also own stainless steel bottles that have carabiners attached that I can hook onto anything.
My plan is to use my resort mug, hook a carabiner on it, then attach it to our park bag. Simple, eliminates the post-breakfast trek back to our hotel room, and allows a post-park refill on our way back to our room. We will just refill that with water all day instead of a conventional water bottle.
Alternatively, I'll use my collapsible travel water bottle. It's nicer for walking around when half empty as the liquid doesn't slosh as much. It has a carabiner which I typically hook onto a lanyard.
The other simple option is to just pop your bottle INSIDE your bag. The pros to this is that it won't swing around and the weight will be better balanced.