Not knowing where you live, I wouldn't know your codes, or the heat load requirements. An experienced HVAC man in your area can advise you better- and I think he did.
A 4" duct is good for about 50 cfm.
It all depends on your climate, attic insulation, humidity, windows, exterior walls (east, west, ect) lights, floor type and so on. I could only guess that a 4" duct would do.

Use what you already have and add a damper to reduce air flow.

You can use a 6 x 4 reducer off of the existing Y. Attach a four inch flex for the bathroom. The floor register can be 4 x 8. Using four inch duct is acceptable.

The smallest we install is normally six inch to baths and closets. The other rooms are normally seven inch. All of our ducts has an A-collars with dampers. Seven inch gives us better control with air distribution.

Phillip
www.ptcooper.com

Thanks for the info so far. Sounds like maybe I should go with the 6" and a damper with a smaller register.

To clarify - should the damper go as close to the beginning of the bath branch as possible (near the Y) or does it matter?

I had thought of a damper as a possibility, but was concerned with placing a damper in the crawlspace simply for the lack of accessibility if/when it needs to be adjusted.

My crawlspace is almost absurd on the entrance opening and actual space under the joists. That's why I'm trying to do as much as possible while I have the bathroom floor open - much easier access.

For what it's worth - my location is southwest MO (Springfield), the bath's exterior wall faces south and has one glass block window in it that's 32x40". Lighting will probably be two overhead lights (one in shower), and two wall lights over vanity. Floor will be tile. Fiberglass insulation will fill exterior and interior wall cavities.

In that case, I would use the 6" with a damper or adjustable register in a pinch.
If your already having airflow problems with the bed room, this could make it worse.

Best practice suggests placing damper at beginning of run. For ease of adjustment, put it in the best place that can be accessed once or twice. If you have room for the larger duct, use it. Nothing special about the logic, use what you have available. Otherwise the run will cost more, yet do the same cooling. The bath will not need as much air as other rooms. A lot of air will make you cold when drying off. I would probably never put a return in a small bathroom. If it was 100+ sqft maybe yes. A return in the bath will cause mildew in that duct. Difficult to design a return, so most installers don't use one in the bath.