Earlier quoted context omitted.
I have to be honest. I'm seriously doubting that math you didn't do. In my experience GPS murders small batteries. And putting large batteries on bikes seems like a nonstarter for bikes that aren't electric assist.
But the GPS only needs to be active when the bike is a) moving, with b) the BLE phone connection absent. There are ultra low power motion sensor ICs that literally have a GPIO for "motion detected". Put that on the reset pin of your CC2541, and you'll be set for months of battery life.
Switching it on for a minute or so every hour if outside BLE range could help, but would make it harder to locate your bike fast. Maybe, it should start at a 100% duty cycle, and drop off over time? (Clock drift shouldn't be a problem. The device has GPS, so it has an accurate clock)
And you need to filter that 'motion detected' thing, or your bike will keep resetting itself, even before it can check the BLE connection. Or is that something that the sensor ICs can do for you, too, nowadays?