Companies do not have blanket non-compete clauses. You may individually have one based on the contract you signed, which may depend on which company you originally joined, and also whether you subsequently accepted a different contract during an internal move.
That clause, if you find it in your contract, may not be enforceable depending on your jurisdiction. I had a solicitor read mine (a relative who did so free and informally) and they said I could either strike through some clauses or assume they weren’t there, because they were not legal in my country.
Finally, if you’re high enough in the organisation that anyone would care about you joining bloomberg, you should already know.
In other words, this board can’t answer your question, but it’s likely that no-one would notice where you went - nothing personal, that’s just how it goes.