Straw VS bark for mulch in garden N?

Will straw/hay tie up N if it gets incoporated into the soil like bark does? Thinking of switching to hay because I find using the bark chip I am always inadvertantly mixing it in to my soil which I understand can bind up N for a period of time. Bought some bales to set up for a cold frame and thought I could pull them apart for mulch down the road. My thinking is the bales will preform 3 different duties over the season, 1 - cold frame walls, 2 - mulch during heat of summer and 3 - organic amendment (thinking any organic matter brings "something" to the table).

And what is a good price for a bale?

Thanks
Nadine

First of all bark does not tie up N, wood chips do, but not bark. Straw is best and hardly affects N uptake. Hay can be a nightmare with the seeds in the hay. Stay away from this. Price varies widely. Here in montana hay bales are 1.25/bale. Down your way 8.00.