First, don't assume being able to bid will get you the days off you want, especially if you're a newbie. This is still the airline world and paying your dues is part of the game to a certain extent. You signed up for it now make the best of it. Your best bet is to take a look at the reserve tab on sked+ and offer to switch to a day they have less coverage. You have to make a case why it helps them. If it doesn't in a noticeable way your answer will always be no.

Second... This comment makes me wonder how strong the kool-aid is during indoc these days. In ORD there is rarely open time on the CRJ despite horrendous levels of reserves. You shouldn't live in fear of your employer canning you because you have a life outside of work, especially as a new hire. Everyone is desperate to get guys in the door. They aren't going to fire people, but scare tactics do a decent job of keeping the masses in check.