Hmm... I wonder if Baku have some health issue and I think the nosebleed might be a symptom.
Actually, I was wondering about Baku health ever since I saw how fit Hal is during the battleship game and how not fit Baku is. I mean, during the abandoned building gamble he have to be carry up the stairs by Kaji! I don't expect him to be as fit as Hal, but he should at least have an average physical strength.
I can't see Baku neglecting to work out and just completely rely on Marco or Kyara for strength. This is a guy who learn morse code as well as how to mimick people voices just for probable future gamble. I would expect him to probably learn a few martial art to defend himself just in case.
Overall, Baku is portrayed as a weak person. But why. Hal learn to fight (probably) for gambles so why don't Baku.
At first, I thought it might be because the author did it so Baku won't be too OP and give others like Marco some spotlight. But in some cover arts, you can see that Baku have abs, so he clearly is fit.
Which lead me to think that Baku is fit but due to some health conditions, cannot fully utilise it.
But that is assuming that the cover art is umm... canon? I mean we never actually saw Baku topless in the actual manga pages. Plus, the only evidence/symptom is the nosebleed. I know this is a common manga trope and I did saw some comments explaining that Baku is just excited. Maybe he have some conditions where stress/excitement cause blood to bleed?
I don't know. It's just too weird that if Hal trained his body for preparation, Baku wouldn't do the same. Or at least have an average physical strength.
Edit: Re-reading a bit, I found that during the "real" labyrinth gamble, where there was a trap room with depleted oxygen level. The referee said that Baku manage to raise the oxygen to quite a safe level, but jokes about how Baku have a weak body because he is really affected by the lack of oxygen.
At the abandoned building, Baku also showed a lack of stamina rather than lack of physical strength. Also at the tower arc, he fight against his opponent a bit. (He grab his hand when he was choking him and also push him down the stair) He strength may be average but he's not too weak.
So maybe he have problems with his lungs? Then the nosebleed can also tie into this.