I have three thoughts:

1. First, keep in mind that 'cycle commuter' is certainly not a protected class of worker (such as workers protected by gender or race) so frame your approach within the view that you are not asserting a 'right' here.

2. Consider that your boss has a legit point. Personally I would be unhappy having to be the guy risking a violent robbery for what I assume Starbucks pays you. Being on a bike makes you an easier mark. If I was a criminal and I knew you carried the bank deposit then it would be pretty easy to simply run you over and take it.

3. The appeal to Starbucks environment stewardship commitment is probably your best bet. But do not be surprised if Starbucks asserts that your safety is a higher concern (but not high enough to use an armored car service).