Sources are inconsistent on this topic – some say Turkey has closed the Straits to all warships, others say it has only closed the ships to the official parties to the conflict, which is currently only Russia and Ukraine (arguably Belarus too, but that's irrelevant to this, since as a landlocked state they have no navy), and that other naval ships, including Bulgarian and Romanian, are still allowed through, so long as they don't actively join the war. I'm not entirely sure which set of sources are right, but I suspect the sources claiming a narrower closure are more likely to be correct.
Putting that aside, even the official parties to the war are allowed through the straits to return their ships to their home ports (unless Turkey is directly involved in the war, in which case Turkey can block all enemy vessels, even those returning to their home port). Since the only coastline and naval bases of Bulgaria and Romania are on the Black Sea, that rule covers their entire navies. It only really disadvantages Russia, since Russia is the only Black Sea state (other than Turkey) with naval bases outside of the Black Sea. It means Russia can't send reinforcements to the Black Sea from their Pacific, Baltic or Arctic fleets.
In a scenario in which Romania or Bulgaria actively joined the war, it would be a direct Russia-NATO war, including Turkey. In such a dire scenario, Turkey would likely announce the unilateral suspension of the Montreux Convention for the duration of the war, and allow NATO warships unlimited passage. Russia would consider such a unilateral suspension of the Convention to be an act of war, but in such a scenario Turkey and Russia would already be at war anyway.