I'm not sure what you mean by "private bedroom" but if it involves closing off a space with walls and doors, I'm finding it at about 30 feet overall length. Less than that, you might find a bed at one end closed off from the living area by a curtain door, around 22-25 feet length.
Here is one lightweight 30-footer that might meet the need:
White Hawk 27DSRL. In this one, the bedroom is further isolated from the living area by a large (for RV) bathroom.
This one
White Hawk 27RBOK puts the bathroom at the opposite end, but gives up a lot of interior space to an outdoor kitchen and puts the TV in an awkward position relative to the seating.
Forest River's Rockwood Ultralite line has similar 30-foot floorplans like this
2604WS or
2608WS.
For other relatively large lightweight trailers, look at Keystone's Passport Ultralite line.
To get down to $10K to $15K, you may be looking at the used market. These particular models won't be found, because model lineups and even model line names change frequently, but these larger (27-32 foot) ultralights have been manufactured for at least 10 years. Jayco was using the Jayfeather and Eagle Ultralite brands previously. Gulfstream used the Streamlite brand, while Forest River's base-level Flagstaff and Rockwood models have been lightweight for many years, even before "Lite" branding came into vogue.
