You have already been given good information -- if you check eBay Collectables - Vanity Perfume and search for Atomiser bulb - you will find many modern equivalents. I think all these are made to a standard size, so really if you buy the cheapest one in an agreeable colour it should fit your bottle, especially if it is only wanted for display. If it is wanted for use - I would have to ask - why? In their day they were inefficient and wasteful, and the bulbs perished quickly. Unless I am missing something, this is from a dressing table set - it would not have held a specific perfume, but would have been filled by the consumer with their favourite perfume. It may have an etched mark on the base somewhere but that would be from the glass manufacturer. Or it may have had a glass manufacturer's paper or foil label, that has been lost over time.
