I suggest you consider the Federal Joint Travel Regulations for reimbursement of a privately-owned vehicle per mile.
http://perdiem.hqda.pentagon.mil/per...aqpovpast.html
Currently, it is $0.505 per mile and going up, of course. This rate considers gas and maintenance. Divide that rate into your bicycle price (and any outlay for accessories). This quotient will give you the number of miles you need to ride to break even. So, assuming $500 total outlay, you're looking at about 1,000 miles.
You can then divide your round-trip commute mileage into that to give you the number of commutes you need to make. Subtract whatever mileage errands you'll make. But, I wouldn't stop there.
Now subtract from your previous quotient the reduction in gym membership, less "junk" food...etc. Now consider how you feel from riding...priceless.