I hope this message finds you well. I am a licensed attorney with over a decade of employment law experience. It is a pleasure to assist you today with this issue.
The answer to the question actually lies at the feet of the company that owns both hospitals. As a matter of course, one could argue that the non-compete is no voided by the purchase by a new management company. However, that can depend on the nature of the contractual language both in your non-compete (sometimes there are savings clauses that carry this NCA forward) as well as the language in the buy out agreement relative to new ownership.
That said, you are in a better legal position now, since the ownership of both entities is one in the same, than you would have been had ownership not changed. You now have good faith arguments predicated on equitable grounds to justify the move without having to pay back any bonus as well as to not violate a non-compete.
I suggest a sit down with hospital management (I know - pain in the rear) to discuss the matter. The order of discussion should revolve around the bonus first (the bonus would have been owed to a different company - that is no longer relevant and should be a moot point now under any circumstance). Next is the issue of the NCA. I could see management from the hospital that you would be leaving being upset. As such, you need to be able to make the argument that for the master company, what you bring to the table from an earnings standpoint will be the same or greater. Your position of argument is actually higher than the two hospitals. It is from the perspective of the company as a whole. In so doing, you can also argue, with a straight face, that the NCA pertained to the old company - not to the new ownership - and is therefore legally moot.
So, the answer is yes, you can legally argue for non-repayment as well as to the invalidity of the NCA as a whole under the circumstances.
Let me know if you have any other questions. Please also rate my answer positively (Three or More Stars) so I can receive credit for my response - otherwise I will receive no credit.