Just found my first mushroom biome ever in my new singleplayer game, it's a small chain of three tiny islands, with only two naturally occoring giant mushrooms, one brown one red, each on opposite sides of the chain. Did plant and grow one red mushroom for the fun of it though.
Took me about... a day and a half worth of traveling in one direction i think? i left one day, kept sailing through the night, then all day again, and now it's the seccond night when i found it. Took a screenshot of the cho-ords, so hopefully i can find it again at some point. i'll need to come back after enchanting a silk touch pick or shovel so i can grab some of the micillium.
No mooshrooms however sadly, not a single one. ahh well, would have been a huge pain to bring them all the way back home, and i don't have any wheat on me anyways :P