I've renovated almost 2 acres in Sunstar common Bermuda in the last 4 years. You can read about my renovation here: http://www.lawnsite.com/showthread.p...ighlight=avguy
I ran a Harley rake and then a rockhound over my property before seeding and it is still rough in spots. I would be shocked if you could run a reel mower over your property without a little prep work first. Also, Bermuda likes to be fed. Up until this year I put down 32-3-8 at 3.1 lbs/k in June, July & August. Because of the drought conditions we have experienced this year I was advised by my local JD/Lesco guy to put down 5-10-31 for my August app. I'm mowing every 3 days @ 2" with a rotary mower.
Have you had a soil test done? That will help you determine more than anything what your lawn needs. My soil was very acidic at 4.9 PH. It took me a couple of years before I got it where it needs to be. Good Luck! Scott