Ivory? That would be a safe bet to blend with the hall. Then you could add accents in your favorite colors. Ivory with blues--especially a Wedgewood blue tone, might work well.

Paint the bedroom and hall at the same time, and get a color you like. Once you pay a painter to get there, get set up, haul drop cloths and supplies......... you may as well keep on painting. : )

I would go with ivory as well. We just redid our guest room and I went that route. It gives me the option of changing up bedding and curtains seasonally too.

Prime it with a light gray primer to cover the red. You may need two coats. Then paint it the same white as the trim. Once you are ready to paint the hallway, you can change it to coordinate with whatever bedding you choose. The guest room windows look beautiful.