am I able to put my buds in a brown paper bag for drying instead of hanging them upside down? I mean, I don't really have the place to hang them.

yes you can...good ideas here
commonly you have a couple choices. hanging is only for convenience...this method is the 1st option or set them on a metal screen as mentioned above.

2nd step paper bag, 1st option dry until stem snaps. As mentioned above then place them in paper bags, to allow the paper to draw out the remaining interior moisture. (when they feel dry on the outside; they are not dry.)
Of course this brings us to your idea...It is written that alot of growers, hurting for space, and for security reasons bag their buds as soon as they are harvested. Cut budded stems into manageable pieces and gently (trichome damage) place them in paper bag. DO NOT cram them in the bag...Handling them alot is not a good idea.

You must open the bag once/2wice a day to let fresh air in.

Last...glass jars...wait, a quick recap.
harvest,
hang until stem is dry enough to snap 5-10 days (best way, but optional) or,
harvest and cut into manageable pieces and place directly into paper bag. 7-14 days
Last..OK, We should be on the same page.
Place dried buds in Glass jars to cure...CAUTION/// If you place buds into Airtight glass jars before they are dry enough, then you face the possibility of the buds molding.

so, Yes; You can harvest and place your buds in a paper bag until it is ready to smoke...Not the best way, but It will work just fine. I treat all my trim this way.

I have also used the Metal screen method and find it to be another great option for drying bud!

I gotta go. lw