I am just wondering how the people out there clean their mop's when they are done with the bbq
Personally I prefer a mop over a brush. I think that you get your sauce on whatever your slathering quicker, and therefore get the lid closed faster. I also feel you can apply a thicker/heavier application of said sauce.
I'll take you through a typical course of events for one of my mops.
Remoce from your holding device (drawer, appliance carousel, hanging hook, etc.
Wet said mop with water. THIS IS IMPERATIVE, so your sauce stays on the surface and doesn't soak in too deep.
Squeeze excess water out.
Use as directed until you, and the rest of your dinner party are stuffed to the explosion point.
While holding on to the handle grab and squeeze as much of the remaining sauce out of the cotton fibers as you can. This pertains more to heavy sauces like barbecue types as opposed to thin "true" mop sauces.
Get a tall thin glass (preferably non breakable about a 12 ouncer) Under running warm water put the mop in the glass full of water, and slosh up and down vigorously while clean water is still running into the glass. After about 15 seconds of this your mop will be pretty well cleaned. You might see a little fiber staining from a heavy sauce but the next step will cure that.
Place in the dishwasher and run the cycle.
Here's another important part. After the merry go round cycle is complete, I'll do the slosh in the glass routine again. I feel this removes any residual detergent, and or rinse aid that may be in the cotton fibers. This should alleviate a tainted sauce the next time.
Squeeze the water out
Hang vertically after fluffing the fibers a bit with the handle up until dry.
Replace in holding device till you need it tomorrow...
Now here's another thought. Mop or brush. For a heavy sauce (barbecue type) a lot of times I'll actually pour this on the recipient right from the bowl, and just use the mop or brush to spread the goods. This process only works with something heavy that isn't gong to run though.