Pull them up and stir them in and the worms will gobble them before long. Fungi can be a common thing in the bin, generally nothing to be worried over but check if the bin is a little too wet.

I get some large white mushrooms occasionally in my bins. During April and May this year, there were probably well over 100 that started UNDER my carpet bin. The tops were about 6" across, and lifting up the carpet. I did not ID them. I pulled some and tossed them into the bin with fresh manure. Most of them I let be and they are all long gone now.
No worries mate!
Happy wormin' Pete

Fungus in the bin is a good thing. It is one more composter breaking down the cellulose.

When the lawn is really moist, I gather mushrooms that grow and put them IN my bins (chopped). They are eaten up really quickly.

Chuckiebtoo

That is good to know. I won't worry about it, just burying them a bit. :)

Haha, Pete. I appreciate the nod to Australian vernacular. FYI, I'm 100% American who happens to be living in OZ. :)