Definitely not many, that's for sure. The signature in the copy I have doesn't look old, definitely nowhere near 40s-60s. It's also not dated, like Bukowski often did in the early days (e.g. I have a copy of The Outsider #2, signed and dated in '67), so I guess it must be 70s or 80s. Don't have a scan or photo with me right now, otherwise I'd upload it for the more knowledgeable guys here to analyze.
Talking about Story, Scott Harrison once showed me a copy in outstanding condition that was inscribed to John Martin with the words "For John Martin, who found the the still struggling writer 24 years later". Unfortunately I couldn't afford it at the time, and he's sold it since then. Damn shame that.
Just looked up the conversation I had with Scott Harrison on the 'Story' topic back then. He thinks there's probably 10 or less signed copies and has never come across one that was definitely signed in the 40s or 50s.