Well depends what kind of car is it and how big your bag is!
A Scion/Element can stove 2 bikes as is and 2 pax up front.
A Ford Explorer can take 2 bikes + 2 paxs with front wheels off. 54cm frame, larger frame u may have to take off seatpost.
If it's gonna go inside, I don't see the need for a bag, just some bungee cords-like to secure to handholds.