Nobody has to push a button.
The bomb could be triggered by either a simple timer, or an altimeter. Even more sophisticated would be a an altimeter trigger which started a timer so it would go off some time after reaching altitude.
The simple timer could go off on the ground if there are delays. The simple altimeter guarantees everyone is killed, as the aircraft blows up in flight, but most of the time it is still over land and the debris can be recovered, as happened here. The altimeter/timer combination can be set to go off over water which makes recovery and forensics much more difficult.
I vote for theory it was some type of altimeter bomb to make the aircraft was actually in flight before the explosion , not delayed on the Tarmac
The detonation at 31k feet was the same altitude as PanAm 103 was detonated as I recall - sufficient altitude that only a relatively small explosion would set off a catastrophic and violent decompression
But rather than being on a beverage cart That could be moved, I think they would have placed it where it would blow off the tail