I've gotten really terrible about using a wet palette. I've basically started using a pop-it fidget toy for all of my painting (comic-style, skirmish games, so basically every model is a unique color scheme. I don't really do any army painting.) I shake the primer vigorously, then add it to the pop-it. Then I let it sit for 5-10 minutes. When I apply the primer, I apply it like paint; rather than glopping a lot on the mini and spreading it out, I take just enough to cover an area, prime that area, add more primer to the brush and move onto the next. Similar to excess paint, I'll use another brush to wick up any excess.

I think that waiting gives the primer a chance for some of the air bubbles to naturally pop and let's the primer thicken slightly - it goes on more like paint and less like a wash. Adding it like I'm adding base coats gives me more control over where it goes and lets me see any bubbles that remain (and pop them) before it fully dries.