"Many people and many fish swim in Lake Balaton."
Translation:A Balatonban sok ember fürdik és sok hal úszik.
That's how we just say it.xd You could also use "swim" as well, like... "Sok ember úszik a Balatonban". But if you say it with "fürödni" like "Sok ember fürdik..." it means you go into the lake and have fun there, play water sport games and so on. Or just chill in the middle of it you know.
According to the internet, the British meaning of "to bathe" covers the meaning of "fürödni". That is, to swim or otherwise spend time in the water, for entertainment, not for washing.