I cut 'dots' [or squares, or bits of scrap of any shape] from 100% wool felt and glue it down with whatever "crazy glue" kind of epoxy I have at hand. None have come off in 30+ years of hanging art & moving house four times.
On very pointed/raggedy corners or ill-fitted frames, I will cut a shape that covers the entire corner, not just a dot. I like that flexibility with the felt. (The ribbon or sponge methods suggested by virolino would take care of these too)
I like the wool felt over plastic bumps as I feel it prevents wall markings better than the bumps. I have no scientific proof for this, though! Just that I noticed when moving house that my own felted frames left no marks, and the art that came with pre-attached rubber dots lifted dots of stuck paint when removed, where years of trapped humidity & dust had made a tiny seal.
Though I find myself stumped by canvases that wrap around the frame completely, and some are even painted all the way around and meant to be left exposed. No ideas there...
Not sure how the craft store plastic felt would do, I always have 100% wool felt on hand from crafting projects so I use that. Felt dots with sticky backs are sold commercially for framing use and seem to be plastic felt, so using your own plastic felt should be ok.