I have had a little experience with this on scout camping trips. It is a rather common camping problems. If you Google search for "camp toilets" you will find tons of products, but the bucket is about as good as any of the more expensive contraptions, plus the bucket is handy for other uses if you do not need it as a toilet.

I would suggest lining the bucket with a plastic bag. This will allow you to remove the bag after a few uses, twist tie and store or just twist tie and put in a new bag, leaving the tied bag in the bottom of the bucket. Camp bucket toilets can get rank in the great outdoors. Based on my indoor experience with baby diapers, I would think you would like to seal the waste materials rather quickly.

Bleach will work if that is what you have. There are chemicals made for use in camp toilets that thicken the liquids and do a better job of controling the smell. If you have to use what's on hand, Lime is good to help control odor. Kitty litter, potting soil or peat moss help absorb moisture and help some with odor.

I have been on caving trips where you had to pack out everything (EVERYTHING). We carried a bottle for urine and made poop packs. Start with two sealable plastic bags, cut sheets of newspaper to serve as a target and put some kitty litter in the bag. To use, make your deposit on the newspaper, sprinke a litte kitty litter on top, roll up and drop in plastic bag number one., seal and double bag. Pack it out.

If you go back a couple of hundred years, it was common to keep a chamber pot under the bed for night time use which you dumped into the street or gutter each morning. Oh, for the good old days!

During the Civil War, the inhabitants of New Orleans took a real dislike to Union General Butler. Chamber pots that featured his picture in the bottom were a popular item. Adding a photo of your choice to the bottom of you chamber bucket could be a nice touch.