Can I use a single 20A circuit for two bathrooms?
Ed Beal's post covers a major point... here's a little backgrounder on that. A 20A breaker @ 120V will supply 2400 watts nominal.  &quot;Sounds like plenty, what could 2 bathrooms possibly use?&quot;
Well, one hair dryer is between 1500 and 1800 watts.
So while it's perfectly legal for any number of bathrooms to share 1 electrical circuit (one McMansion was built with 5 bathrooms on 1 circuit)... it's a bad idea from a usability standpoint.
So really, decide.  What is the purpose of doing electrical wiring?  To serve yourselves.  If you're trying to barely comply with Code to get inspector sign-off so you can flip the house, then 5 bathrooms on 1 circuit makes sense.   However if you're gonna live there, then the first rule of electricity is: &quot;It's there to serve me, and do my bidding&quot;.  So install the electrical service that you want.

Now, as far as that full panel, first, if you're full it's surely less than 40 spaces.  If  so, it surely allows at least enough tandem/double-stuff breakers to make it to 40... so that's an option.  Also, in the LED age, lighting circuits don't need the ampacity they once did - if you have several lighting circuits, you may be able to consolidate them onto one breaker.
Also, bathroom hardwired loads can be on any 120V circuit of any kind (except the dedicated circuits to kitchen, laundry, garage or bathroom receptacles, or furnace. And they are allowed on the bathroom recep circuit if that serves only this same bathroom).  So it may be possible to recover spaces by diffusing those loads onto other nearby circuits.
Lastly, you can do what you really, really ought to do... and that's fit a big subpanel today so that you are ready later when you want to add other circuits.  You don't want to let opportunity after opportunity pass you buy - hot tub (can't) heat pump (no spare spaces) floor heat, electric vehicle, 240V welder at a great price, have to turn 'em all down.  Again back to &quot;Electricity serves us&quot;.