I agree with keeping shove a bonus action.
With an emphasis on verticality in encounters, this gives melee characters a good way of interacting with that feature by allowing enemies to be pushed off of high ground. Also allows enemies to be pushed into surface effects which also gives melee characters something to do in that regard.
It also buffs the STR stat which is underpowered in 5e (assuming shove is a STR check, I haven't played DnD in awhile).