Which comes first -- bike fitting or new saddle?

[Seajay]

I always start with the saddle. There are only three places where you touch the bike. You don't want a bike fit that is only 66% right. (frankly worse)
I ask very early on..."What do you think of your saddle?" "Does your saddle cause pressure that makes you less than comfortable during any part of your ride?" Can you ride two days in a row without dreading sitting on the saddle at the start of the second day?"

IMO you can't get much of a fit with the wrong saddle.

I've gone so far as to get a client to use chamois cream during the fitting and asked a client to reschedule because she came straight from a spin class and told me "after an hour on the spin bike, I'm sore sitting on the saddle"

Any decent shop will let you try a saddle for a day or so before your fitting.

On a side note...It's frustrating as a fitter when the client won't buy the parts they need to make the bike right. You've invested the time and money for the fit. Don't cheap out by skipping a saddle, stem or handlebar change.

Also....Per Sky King's comment: We tend to have bike fitters here that fit all riders in a more aggressive racing posture, regardless. THAT IS NOT A BIKE FITTER. If he/she is fitting you how they want you on the bike...RUN AWAY!