No, the Word bed is a common noun, a Word for any bed of any kind, anywhere.
A proper noun is the name of a specific person, place, thing, or a title; for example:
- Creek Bed Street, Muldraugh, KY orBed Hollow Road, Roxbury, NY
- Daisy Hill Bed & Breakfast, Nashville, TN
- A Bed of Roses Florist, San Francisco, CA
- "The Bed Sitting Room", 1969 movie with Ralph Richardson and Rita Tushingham
- "Raised Bed Gardening" (how-to book) by James Paris
