To what end? He lives in New York, a solid blue state, and posted his endorsement on his LinkedIn account (heh) unprompted. If he secretly voted differently, a) it wouldn't make any difference and b) he wouldn't be using his influence to encourage people to vote against his secret fave.
I'm not saying this because I trust Bloomberg, I'm saying it because I literally can't see any benefit to him lying about this. Are you suggesting some sort of 4D chess reverse psychology deal where he endorses Kamala so that people who dislike him will trigger his trap card by voting against his publicly supported candidate, which is secretly what he wanted all along?
On top of all that, I honestly can't conceive of why he'd prefer Trump. People like him care about one thing: money. A Trump economy attempting to create autarky via blanket tarrifs would annihilate his investments.
He has no major outstanding court cases he needs protection from and no major government contracts in danger (in either case, Trump might be more useful since he's very bribable), which means the only selfish logical choice for him is Kamala.