As many times as we did this in-house, I couldn't really give a decent guess at what this would cost on the outside.
I could develop some methods in a couple of days that would turn out to be great for our products, and other analytes in certain matrices could take over a month or more. Sometimes columns would need to be obtained. Typically, if we could find anything even a little related, we would draw from literature, we did not believe in re-inventing the wheel.
cGMP Validation studies would follow and would hopefully pass. Validation alone could take a month or more. If your QA is super-anal, maybe triple that. We had analytes that would not degrade under the very-vague published guidelines. We always had 2nd and 3rd operator do samples as well, and used different instruments and columns intentionally.
Figure outside lab costs at maybe $150 per hour. Since ours were done in-house I didn't need to factor in instrument or supplies costs.