Best desk job I ever had was when I worked at Kozmo.com for the guy who is now the owner/founder of MaxDelivery. He is a great guy.
According MaxDelivery's website you do not have to have a mountain bike. This is what the website says:
Originally Posted by MaxDelivery
Delivery Associates - Full-time and part-time positions open for afternoon/evening shifts
We are seeking professional, mature people to deliver orders by bicycle and project positive, professional company image to customers and the general public as "the face" of MaxDelivery. Minimum requirements include riding safely and lawfully, and maintaining courteous demeanor with customers as well as motorists, pedestrians, etc. Must supply own cell phone and bike and use company-supplied front basket or equivalent hauling capacity. Must be able to haul multiple large-capacity orders at a time (orders include large and/or heavy items like cereal, diapers, orange juice, etc.). Prior messenger/bicycle delivery experience useful but not required. Performance-based pay structure. Top performers can earn $10 to $14 per hour.
Here is their employment page:
http://www.maxdelivery.com/nkz/exec/Jobs/Show