seeding bermuda grass.

I do not know where you live but here in the deep south common Bermuda is used a lot. It is considered a high traffic grass. That is why they use it on ball fields a lot.

Common Bermuda grows best with a soil PH of 5.8 to 7.2 and requires about 3-7 lbs of N per 1000 sq ft per year. It can be left to grow long but if you cut it short it is best cut with a reel mower. Other mowers work but a reel mower allows for the shorter more manicured look.

Seeding on a slope may be a problem. A well prepared seed bed is best for planting but then as you said erosion comes in to play. You may try covering with a thin layer of hay to prevent erosion till it can get started. You could also try to over seed with a little extra seed to allow for loss. Normal seed rate on prepared bed is 1 lb of hulled seed per 1000 sq ft or 40 to 45 lbs per acre.

Bermuda needs full sun and does not do well in the shade. Wait till the soil has warmed well before seeding. About 70 deg 2" down should be good.