I think it is worth a try to totally deflate the tire with no weight on the tire (center stand) then re-inflate the tire. Not to change the bead, but to give the tube a chance to put itself in a better position in there, this should have been done at the shop after mounting the tire. Then see if your bouncing goes away.
Maybe your tire is not fully pushed up to the lip of the rim, but it sure is close. I don't see that small difference causing something as drastic as you describe. I change tires for everyone here, friends, strangers, relation, neighbors, and I have a trailer and shed full of old tires to prove it.
Scott