So I downloaded Bioshock Infinite on my steam account, but my roomate would like to play it as well. When the game comes up, there is option for new game and continue, but starting a new game would delete mine. Is there any way that we can both play? Seems really dumb not to just have a file system. 

http://pcgamingwiki.com/wiki/BioShock_Infinite#Multiple_save_games

Please just search for it, it's not that difficult

"Yes Of course those save directories will not work for you because Steam has their own locations. You can find your save data at any of the following locations for Bioshock Infinite on Steam:

C:Program Files (x86)SteamuserdataXXXX8870remotesavedata

OR

C:program filesSteamsteamapps... ahead there will be some subfolders related to your game's name. Check those files."

Copy your savegame to a secure location, then delete it. Your friend will be able to play. Create two different folders for the savegames (one for you, one for him) and make sure to backup the savegame the moment you quit the game. It's a bit of a hassle, but the best solution I can offer.

Also: You have to turn off synchronization with the steam cloud for this game.