Bike commuting comes with plenty of surprise costs, from flat tires to bike theft. Would an experienced personal financier figure out a 'safe' amount of money to put in a savings account for the year's bike problems, or would they try to specifically forecast the costs and make a monthly budget?
I do not meet your qualifications but this is what I would do:
1) Save an amount that can replace your bike and accessories if it is stolen. Don't touch it for anything but that. 2) Compute an average monthly cost for maintenance items, double that for a couple of months until you have the account built up, then budget that amount every month.
If your bike/headlight/front tire, get stolen or broken beyond repair, take it out of the first account. Then your savings priority should be to rebuild that account. I would be a bit alarmed if you have to keep hitting this account for legitimate reasons.
When a tire goes flat, or other normal wear and tear item occurs, take it out of the second account. This account should fluctuate regularly, and it is normal. During certain months you may want to increase this amount (more glass on the street because of outdoor events means more flat tires).
The same kind of thing holds true for a car.
Putting numbers to some figures would help.
I think the most alarming thing about your post is that a theft is somewhat ordinary. Yikes!