maybe give it more air and less water to avoid fungi

what you're seeing may also be actinomycetes bacteria filaments, which could mean the bin [or that area of it] has been warmer than is good for the worms, like the food you're adding is doing some faster 'hot composting' - if it's not heating, don't fret, worms eat fungal mass as well as bacterial mass, so it's not doing any harm

Bill

Well from what I've read, add a layer of bedding. What I use is, I've gotten a bag of shredded paper from work. It's cross shredded too, so I'm guessing that's a plus. I soak some over night, and then lay it on top, or on top of that area. Also I do the same with a bag of leaves I scooped up and saved. So got some brown and white. Read somewhere to mix greens and browns, and I'm sure that has to do with carbon to nitrogen ratio.

So in short, add a layer of bedding and I think you'll be alright, and that stuff growing won't hurt anything and eventually the worms will eat it, I think.

Sounds like cobweb mold. The mycelia look like wispy gray cobwebs(hence the name). You can find many photos of cobweb mold with a web search. Reduce the moisture level by adding more bedding, watering less and increasing air circulation.