Depending on the type of grass, and how much rain you get or don't get, you can get one cutting per year, or up to 3-4 cuttings from your field. Some custom balers charge x-amount per bale, or some will cut & bale it for a certain % of the number of bales. If you don't want to pay cash to have it baled, negotiate "for halves", he provides the tractor, baler and fuel, you give him half of the bales and you keep half the bales. Several options, it all depends on quality of your grass. If you can get it cut, it needs to dry a day or two after cutting before baling it. Its preferrable for it not to get rained on while it is drying, before it is baled.
I don't know what its like in VA, but in OK, the biggest detriment you have is the fact you have ~6 acres to cut. Maybe it isn't worth his time & effort to mobilize to cut/bale 6 acres.
Good luck!