This is the reason I searched for "oozing mycelium" on Google. I never fathomed that I would search those words.
I chose a nice, sunny day last summer to go for a walk in some woods near my house (thus getting me out of the Sun while still being able to claim I spent some time outside) and found some neat stuff. The most perplexing thing I found turned out to be this fungus. The white parts you see are the mycelia of the fungus--masses of fungal roots, essentially. They spread over the substrate, and the fungus takes up nutrients through them. The substrate here is decaying wood.
As for the red droplets on the fungus, I'm sort of at a loss. The closest species I've found is Hydnellum peckii, also known as the bleeding tooth fungus. The droplets of red liquid are there, sure, but that's it. I can't find any images of what the mycelia of H. peckii look like, so I can't compare it; I'm only finding pictures of the mushrooms. Fungi are mostly known by their mushrooms to the general public, but the mushroom is the fruiting body--only a portion of the fungus. The rest of it is underground as mycelia. In the top part of my second photo it looks like there might be the stalk of a mushroom, but I can't tell for sure, and I didn't snap any pictures from an angle that might help me figure it out.
It's been almost a year since I took those pictures, so maybe if I go hunting around in the same area I'll spot a mushroom for this species. I'll get to that after the rain stops.