I found a 1" diameter piece of wood in my garage. I think it was left over from
the clothes rods that are installed in my closets.
I also have a bucket in my garage full of junk that I've found while out geocaching. Old golf balls, tennis balls, a few baseballs, and a couple of Frisbees. I took a tennis ball, used an Xacto knife to cut an "X" in it, then made the cuts big enough to push the wooden rod into it.
You could also use the handle of a wooden spoon or something equally strong.
The idea is to be able to compress all the plastic into your bottle without
damaging the bottle or your hands.