Is it possible that Yuumi Master is Bard

That's not a Bard tunnel. That's a portal to Bandle City.

With her bio revealed, this theory is out the window. Yuumi's master was a Yordle enchantress named Norra.

My friend brought that option up, actually! And it's interesting to consider. But I think her master is a yordle, specifically a yordle (most likely a female) we don't know about yet.

I think her Master is a Fish could be fizz kench or nami since she was talking about fish

I mean it's a fun theory, but not really plausible. Bard is a vagabond and a cosmic hobo. He's pretty much unknown to most people, and his methods of communication are lost to mortals. I don't think he has followers, let alone apprentices. He does things for his own, or perhaps more enlightened reasons, and I don't think apprentices or anything of that sort would allow him to be as free spirited as he needs to be.

I think it was the Hammers owner before Poppy. she says "You smell kinda like my owner " and " my owner is about your size" to poppy on first encounters.