That's a tough question. For Trump there is a cast of possibilities which have been well canvassed as for gender, regional balance, age, experience etc. The candidates who ran against Trump and lost would, unless they are utterly devoid of honor and can be bought, not be available for Bloomberg as they signed the pledge to support the nominee.
It is hardy beyond the bounds of possibility that the disaffected Establishment may give a nod and a wink to Mitt Romney to pair up with Bloomberg though.
Whether such a pairing from Hell would hurt Trump, or make his supporters even more determined to vote is moot, but I would be confident such a brazen attempt to steal the election from Trump would be a disaster for the Establishment and destroy the GOP.
"Republican" Bill Kristol joins with Leon Wolf to support Bloomberg if Trump is the GOP nominee. These people are worse than scum
Best for GOP, if Trump's nominee,"would be for Bloomberg & a conservative candidate to run." @LeonHWolf has it right http://www.redstate.com/leon_h_wolf/2016/02/27/trump-wins-nomination-gop-better-hope-third-party-run/ …
There is not so much speculation about Hillary and especially Bernie's running mates (except for this light-hearted poll) as, as with much about the Democratic contenders there just doesn't seem to be that much interest.
However a Bloomberg run is of much interest as he will certainly draw votes from someone. The initial analysis is that he would likely draw more from the Democratic candidate than Trump.
This opens the possibility of nobody having the required 270 Electoral College votes and the House deciding the presidency, and also for Trump to win New York State which would, almost certainly, give him the presidency.
So there is a lot at stake. A fascinating concept, and there is even "Chaos Theory A Sanders Bloomberg Trump Three Independent Party's" to add to the mix in this unprecedented campaign.
Which direction would Bloomberg go for a running mate? A Republican like John Huntsman or Former Governor Sununu to show he is not entering the race to bring down Hillary?
Or a Democrat like, the disaffected former Governor of Virginia Jim Webb who has toyed with a third party run himself. I have put the few options I can think of in the poll below but have left an open option for voters to pick who they think might be Bloomberg's choice.