This paragraph below is from the California Building Code and it covers house attached garages. Its last sentence clearly states that a sleeping area door may not open directly into a garage. So, theoretically, a vestibule acting as a divider between a sleeping area and a garage will comply with code because the door will not provide direct access between those two areas.
I said theoretically because there might be some exemptions enforced in your particular jurisdiction, so before starting this work give them a call or make a sketch of your plans and show it to them. They may also require self closing doors on both sides (not only the garage end) of a vestibule and a Carbon Monoxide detector installation in this bedroom (this might be a requirement in your area anyway).
There are also emergency escape and rescue opening requirements; sleeping rooms require such opening. If that room you’re talking about becomes a sleeping area, the escape door cannot open into the garage; even if it opens into vestibule, the only escape route would be still through the garage. A window (if there’s one in that room) could be used as an emergency egress if it conforms to your local safety code requirements.
As for the vestibule dimensions I can’t find any references to a residential construction (and California), the minimum width of a residential hallway shall be not less than 3 feet (914 mm), that’s all I was able to find.
ATTACHED GARAGES [CBC 302, 312.4)
A fire separation is required between a residence and an attached garage. It may be vertical or horizontal or both or of whatever form may be required to completely separate the residence and the garage.
Where any part of the separation is horizontal, any walls or columns which support the horizontal portion must also be protected. Protected walls must have 5/8" type X gypsum wallboard on the garage side of the wall. Ceilings framed at 24" o.¢. must have two layers of 5/8" type X wallboard, but those framed at 16" o.¢. only need one layer.
Resilient channel (RC channel) may be installed @ 16" o.¢. perpendicular to 24" o.¢. ceiling framing and covered with one layer of 5/8" type X wallboard. Any door between the house and the garage must be self closing and be a 20-minute rated and labeled door or a minimum 1 3/8" thick, solid wood door.
Where self closing hinges are used, a minimum of two self-closing hinges are required.
A door from a sleeping room may not open directly into a garage.