I'm wondering how I could make a mud pit. One that's not too deep, maybe only a foot or so. And are there any ways to change the color of the mud, like certain types of dirt?

I'm leaving out some details but you can probably figure it out. Experience is a great teacher -

Dig a hole about the size of a large bathtub

Line it with a heavy tarp

Get six 20 kg bags of pottery clay from a ceramic or art supply store

Mix the clay to desired thickness in a wheelbarrow and dump it in. Use concrete dye to change the color as you mix it.

Get a 4x8 sheet of pressure treated plywood to cover it when not in use. Take care of it and it will last about as long as you will.

Occasionally add salt to keep weird shit from growing/living in it too right?

or get half a dozen straw bales, make them into a rectangle or square, line those with a tarp, above ground, saves a lot of digging.

Nope. Clay is anaerobic There's no oxygen in it to grow anything. Might add a touch of chlorine bleach to the top once a year.

That's a good one too but if you want it to last that hole is hard to beat and straw bales do attract critters. Around here you are virtually guaranteed to have a wasp nest under that tarp before long. There is of course another option that avoids digging. Visit a junk yard, salvage store, used building materials place, and get an old bathtub. An old steel enamel bathtub is good for decades. A modern fiberglass tub is much lighter so it's easy for a skinny dork like me to handle solo. You can frame up whatever you want around it and make it look kind of like it belongs.

Its all personal taste of course, but I'd find a bath tub too small for me! No room to thrash and squirm around. With a liner you can tailor it to whatever size you want. Potting clay is amazing stuff but very expensive; cheaper if you bulk buy. The other option is top soil. You can buy it by the bag in garden centres.

Not sure about clay but there are plenty of anaerobic bacteria so could be worth a check to see if any of them can grow.

I"m not sure how you could check that. Based on personal experience with far larger quantities of natural and man-made clay that's been in one place up to 15 years filled with naked ladies in sub-tropical environment you don't have much to worry about.

I presume that pottery clay doesn't have enough organic material in it to sustain those anaerobic bacteria. It's those that are responsible for the black colour and smelliness of bogs, marshes and mudflats, and I'd guess that salt doesn't affect them so much, as tidal mud can have that in abundance!

We've still got a couple of brick factories around the
Redhill Valley.. great fine dust that makes fantastic red clay.. Stains everything beyond salvage.. so might as well rip em off...