How many receptacles can I place on a 20 ampere 120 volt breaker?
There's no limit to the number of receptacles that can be on a circuit in a residential dwelling.  Code does specify a minimum number of receptacles required in a room (NEC 210.52(A)), based on the length of the walls. The code does not, however, limit the number of receptacles per circuit.

In industrial/commercial spaces, 180 Volt-Amperes (VA) is used when calculating receptacle loads.  This value is often used as a guideline in residential applications as well.  For example, given a 15 ampere 120 volt circuit, you could have 10 receptacles @ 180 VA.

15 A * 120 V = 1800 VA
1800 VA / 180 VA = 10

So a 20 ampere 120 volt circuit, could have 13 receptacles @ 180 VA.

20 A * 120 V = 2400 VA
2400 VA / 180 VA = 13.333

These numbers are simply a guideline, and have no real meaning in residential dwelling units.



You will have to keep the bathroom and bedroom circuits separate, and the bathroom receptacles will have to be supplied by at least one 20 ampere branch circuit (NEC 210.11(C)(3)). So you'll need at least two, 20 ampere branch circuits. One for the bathroom receptacles, and one for the bedroom receptacles.