Check out REI almost all of their gear is good. 1 C note is not much of a budget for down bags but will get you a decent synthetic one. Also check out Sierra Trading Post for some good deals, stay with the name brands as they have a range of quality. This one fits the bill: https://www.sierra.com/kelty-20-f-tuck-ex-thermapro-sleeping-bag-mummy
Bags I have owned or used and liked were: Sierra, North Face, Marmot, REI, Jacks Bags, Kelty, Big Agnes and some others I don't recall. I have one that is forty years old with lots of duck tape patches but still good. All the synthetic bags didn't last half as long. Get a tall one and if you are not used to a Mummy get one with a box foot to it, a semi mummy.
Get one rated for three season use as I have had fairly heavy snows in Yellowstone even during the summer. Also get a self inflating foam mattress like a Thermo-Rest, they really make a difference.