I want to make a point here about safety.
Safety first. Operating a motorcycle is much more dangerous than operating a passenger vehicle. The NHTSA puts out a stat of 37x more fatalities per motorcycle mile than passenger vehicle mile.* And operating a passenger vehicle is usually the most dangerous activity people regularly engage in. Another study showed about 60 fatalities per 100,000 registered motorcyclists per year.**
Figuring you'll use this for 3 years, we're talking about a 0.18% chance of death, versus a .005% chance in a car. Insurance and other actuaries normally put the value of a human life around 6-7 million dollars. Let's take the low end at $6,000,000. 6000000*(.0018-.00005)=$10,500.
You may see the risk as acceptable. It may not, in fact, be the biggest risk you take on a regular basis. You said USAF, which could mean a relatively safe position servicing aircraft. Or you could be a PJ, which is decidedly not a safe job. If the sole reason for switching is financial, then the risk to life has to factor into your cost/benefit analysis.
I don't mean to play the card of "this is a risky activity and therefore don't do it." But risk is a real cost. It does matter that you're more likely to die riding a motorcycle than driving a car. If you're asking from a purely risk neutral perspective, you shouldn't switch to the bike. But your risk tolerance may vary. And if it's just about the money and nothing else, don't do it.
But if you sincerely enjoy riding a motorcycle, that could be worth the extra $7500 ($10,500 less $3000 savings you postulated) in negative expected value for you. Just be aware that's what you're paying in risk.
*
http://www.health.ny.gov/prevention/injury_prevention/children/toolkits/motorcycles/nys_motorcycle_data.htm**
http://www-nrd.nhtsa.dot.gov/Pubs/809-271.pdf (PDF, page 8)