Not all bias is conscious, or intentional. The hair dye may not be a bad idea, just temporarily, during the search. Get a pro though, obvious shoe polish color is, er, obvious.
As a 48 year old developer with a lot of gray hair...I've never seen anyone with dyed hair where it wasn't pretty obvious. To me it makes you seem a bit desperate.
That's the thing though, if it was done well, you didn't see it. Ask a few women, that already trust you, if they dye their gray... especially the ones you think don't.
Would one not have to keep up the dyeing if hired then? You don't think they'll notice a rapid change to grey?
They'll notice, yes. Anecdotal, but my experience is that age discrimination tends to mostly manifest at hire time. They think you're too expensive before even throwing numbers. Or too rigid, etc. Things that shouldn't be an issue once you're there.
Even if they don't explicitly avoid older people, there are biases that they might apply that they're not even aware of.