My Mom's in a home with dementia and is incontinent both ways - is this normal?

You're in a unique position to give your mom back some of her dignity that incontinence takes away. You can do as Maggie suggested and joke around with her or reassure her that it's ok, that everyone has bowel movements and it's a normal process for the body. And while you're washing her and changing her you don't smell anything, the smell doesn't bother you. You're calm and matter-of-fact. When you're all done make a little joke like, "There ya go! Clean enough to eat off of!" or something else silly.

I agree with Maggie, when my mil needed help showering, I tried to make jokes , talk about anything, lighthearted that could distract her from the fact she was naked and needed my help. I have very fond memories of those times. When I first started her caregiving a good friend gave me this advice - always use disposable gloves ! It made a big difference to both of us, when she needed more personal help. Hang in there and God Bless

Dementia in the family is indeed a very hard situation to be in. The less you know about the disease, the harder it will be for you to adjust and to be able to adapt to the changes that you have to undergo to be able to prepare yourself and the other members of your family about the changes that you have you go through for that special person in the family who suddenly has special needs.
Dementia is a degenerative disease. There will be times when you feel like your love one is normal and there will be times that you feel that your love one seems to be in the edge and in a hopeless place. Do not think that way because this will just make the situation even worst. The more practical and the more knowledgeable you approach this change in your family; the easier it will be for you, your whole family and that important and special person to adjust to this challenge.
Whether your Mom is at home or is being cared for in a nursing home, your support, both emotionally and physically will make things more pleasurable and easier for her. This is a challenge of course and a bigger challenge on your part because you have to continuously endures the fact that your Mum is already starting to lose precious memories of you, the life that she once had.
Feeling embarrassed of having to rely on other people for taking care of themselves is really a very hard experience to go through. Actually, this is a good sign on your Mum’s end because this simply means that she still has that capabilities for judgment and still has that capability to feel emotions like being shy and awkward; something people with dementia is not capable of. Of course, you need to constantly remind your Mom the importance of being attended to by you or a professional for her safety and wellbeing.
It is pretty normal to feel like you are taking care of a child, but this is your Mom we are talking about. Back then when you were a child and you are incapable of doing things for yourself, she was the one who was there for you and the one who had to give you a bath every day until you were old enough to bath on your own. This is just a simple way of giving back to the sacrifices and the things your Mom had to do for you.

That's exactly what you've got. A child all over again. Except one with dignity and pride. Mom always took her cues from me. I'd blabber on and on as I was cleaning her. I'd tell her this was my pay-back for all the diaper changes I put her through. Joke with her some.

In my case, had I been embarrassed for her...or repelled by it...or in any other way negative? She'd have been mortified. I wasn't, so neither was she. I think "very matter-of-fact" is the key.

I completely sympathize with you. It's not easy watching our parent(s) go downhill. You were caught in a real dilemma expecting company. I hope you don't cut down on her social outings with others. I just know how much it means to her. It probably broke her heart that that happened. Your friends will understand.