Bear spray should absolutely be carried on the body, not on the bike. I work in a wilderness park with a high density of both grizzly bears and mountain bikers so this my bread and butter. If you are on a bike, the most likely scenario is startling a bear and getting knocked off the bike. In the most recent attack we had, a biker rolled between cubs and a sow and was attacked before they had time to react. It was the rider’s partner who discharged the spray and saved them. I’ve also had to quickly ditch my bike and back down a trail after spooking a bear. Doesn’t matter the species of bear, if you startle it in the wrong situation it can trigger a defensive attack.
Bear bells are kinda useless, research says the human voice carries farther and is more effective at alerting the bear to your presence. It sort of sucks to be constantly hooting and hollering on a 6 hour backcountry ride, but it’s part of the experience.
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I guess I didn’t answer the question, but I just carry my bear spray in a regular holster on my belt or waist pack because that’s what I’ve trained to use. Never bothers me during a ride.
Out of curiosity here: human voices carry further, yes, but would you continue to yell when you are riding uphill or doing downhill just in case?
I would expect that bells make it less likely that animals are startled as they can hear you approach from afar.
I yell all the time, mostly on downhill and flats, but uphill if you have enough breath too. Depends on the section of trail and sightlines, etc.
Maybe “useless” is too strong, what I’m saying is don’t rely on the bear bell to make enough noise at the speed a bike travels. Keeping your disc brakes nice and squealy helps too 
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This might make for some tricky descents but should be loud enough to make my presence known to all within a square mile.
Oh, I wouldn’t rely on it, it’s just an additional layer of my safety onion. The closest call was when a bear disappeared in the bushes about 10 m from me when I was barreling down and I thought keeping going was the safer option. (I cannot outrun a bear, but on a downhill, I can, potentially, outbike it.) I’d like to think that the bear could hear me and wasn’t startled/didn’t panic.
Not that I could ask him/her 
The other encounters my primary defense was distance. I simply turned around.