Burning won't hurt the bluestem. I am not sure if individual seeds are affected, but it probably depends upon the burn.

Bluestem tillering increases after burn... and the total mass of the bluestem increases significantly two years after a burn. I don't know if this increase is due to the number of plants (ie. new seedlings) or if its due to stimulated growth and tillering of existing plants. I would guess that its a combination of the two.

A 3 year burn cycle is commonly recommended...

It depends on the amount of dead vegetation and weather during the burn. I have seen burns that only burned off the top, leaving viable seeds and litter on the surface. If there is a fair amount of bluestem, you probably will burn the seed on the ground, but if there is a layer of dead vegetation over the seed, most of it will rot anyway. The season after a fire, you will get many more seeds and great open soil with little thatch - perfect conditions for the seeds to germinate. Yes, seed will germinate after the burn, but most of it will be 1 full year after the burn.

Not really my area of expertise but I have read in connection with many invasives that herbicide after the greenup that follows shortly after a burn is often more effective than one or the other alone.

Here is a link that might be useful: Weed Control Methods Handbook