When I use to wear diapers with tapes, or snaps or pinning, I would stand against a wall (or bathroom stall divider) and put the back of the diaper between my butt and the wall and have it sandwiched between the two to hold it in place. This allowed me two free hands to bring up the front between my legs and tape or snap or pin my diaper up. Then it is easy to just pull my plastic underpants up over them and then put on my pants over that. For changing it is about the same, though urination is all I ever do (not into the #2 mess).
A plastic bag can then take any used diaper and then be packaged away (for washing later) or disposed of in the garbage. It never bothered me if another man was outside the stall waiting to use and suspected I was changing / putting on a diaper / plastic underpants. They can suspect all they want.......