I would actually suggest a different tactic. Call the hotel directly and ask someone to measure the doorway and call you back with the measurement.

The trouble with giving them the answer up front ("is the bathroom door at least 28 inches wide?") is that it's so easy for them to say yes. A question like "Exactly how wide, in inches, is the bathroom door, and remember to account for the obstruction of the door itself?" has no obvious answer, so someone needs to go measure.

And don't ask it like you're asking for a favor. Ask it like you need to know and you expect to get the answer.