My mother is incontinent, unable to make it to the bathroom most times. She wears "pullups" 24/7. How do we offset the odor of these?

Pamela, vinegar is a great odor killer. It kills the enzymes that cause the smell, so once it dries there are not odors, not even vinegar.

If mom is able to bag the depends when she changes then that will be incredibly helpful. It can be done in a used grocery sack or you can buy boxes of those bags online or a restaurant supply store if you can gain access.

When you say that she doesn't make it most of the time, do you mean that she is leaking on her way to the restroom? Vinegar water to mop will help this.

Many years ago, before all the fancy kitty litters, I would put baking soda in the cat box and that really helped absorb the odor, so you can try that in the bottom of a new bag, might help. I recommend that you spray the can before putting the bag in, use lysol or equivalent to keep the odor out of the plastic and wash it with hot soapy water every so often.

You can also put some of those renuzit odor absorbers air fresheners throughout the entire house. They are the ones that look like little Christmas trees and people used to make cute covers for them. These are readily available at wally's world or any dollar store. They are subtle and work really well.

Best of luck finding a solution to this unpleasant problem.

Use smaller bags for each pull-up and tie them closed and take out each time. It may be a hassle but it’s the only way we found to prevent odor. We found small bags that are scented, inexpensive, on a roll, at Walmart

I buy a big roll of 350 produce bags from Amazon for about $11. I put the used diaper in a bag after each diaper change, tie a good knot, and toss the bag in the outside trash bin right away.

As for getting rid of urine smell on clothes, after washing, I hang the wet clothes out in the sun for a couple of days. The sun is a great deodorizer.

I used to knot each pullup into those little bags that are used for dog waste before tossing them into the lidded trash can, kind of the same idea as the diaper genie.

My daughter uses a diaper genie for her cat litter. You might look into one of those. I’m not sure how it works but she claims it does a good job.
My dh aunt, 94 with dementia and incontinent, usually doesn’t change her depends but three times per day. Each time they are changed, the soiled pull-up goes into a lined basket and is immediately tied up and taken to her larger receptacle in the garage if someone is in the house with her. When she changes by herself, she will put them in the lined basket but isn’t able to take them out. The only time there is a really strong odor is if she has a UTI. But I can always tell if there is a soiled one in her bathroom when I walk into the house. We also clean her bathroom daily so I’m sure that helps.
Increase your moms hydration if possible and get the soiled ones out immediately. Aunt has always saved her plastic grocery bags and we use those when we are there and leave one of the odor control bags for when she is alone.
‘She is seldom incontinent of bowels, so I’m sure that’s much worse.