Webster’s 1913 has no entry under this spelling.
Shades of meaning
Fernald has no entry of its own for bridle-path; he lists it under way.
Where he writes about it:
A road (originally a rideway) is a prepared way for traveling with horses or vehicles, always the latter unless the contrary is expressly stated; a way suitable to be traversed only by foot-passengers or by animals is called a path, bridle-path, or track; as, the roads in that country are mere bridle-paths. — from way