There's two problems with spray in this situation. 1. The same as drawing from a bike 2. winds in ND can be around 20 MPH for weeks blowback becomes a real problem.
Getting the bike in between is the only thing I've heard so far (and one of the attacks was fended off this way for miles).
I might have to pose a question on a biking site about a quicker way to brake because that seams to be one of the major hang ups I'm coming up with with any tactic I can think of
That seems like a really good idea, Most of us here, our biking days are behind us

On the "losing the gun comment I made, I was thinking of having it jar lose from your hand, if you fell over and hit the ground.
This is really a tough question, as I posted earlier, there is just to much going on.
You have 3 separate situations that all need to be dealt with
now1 - Bike at speed on a wilderness trail,
2- Defending against the animal attack
3 - Getting your pistol drawn and into action, with out endangering yourself or others . (more than they are )
Breaking it down like that, it looks like getting the bike between you and the critter takes care of the first 2 and the critter dealing with the bike buys you the seconds you need to draw.
It looks to me like the big problem of getting the bike stopped and you off and stable as quickly as possible.
That is the part that other Bicyclists are more qualified to help you with.
As to the other suggestions of sprays, I would not trust a non lethal response to a wild animal, they have a level of determination that modern civilized humans just can't comprehend.
Look how far a deer will run after being shot dead.
But that is just my opinion, some people are more trusting in "usually", most, and "generally".
Condoms are supposedly 98% effective, I have
2 kids, I don't trust any thing that is less than 100%