You can always try, but it doesn't often work with the good, in-demand private tailors. They'll just refuse your business. I didn't use Jenny, but sometimes Fei Fei (mixed feelings about her work) and a guy named "Tailor Chen" who didn't have a retail shop but only did house calls by appointment (no English spoken). Their prices for various services were pretty well set.

Frankly, it's d@mn hard to find a great tailor and especially for women's clothes, and I'd rather have the relationship than quibble over what's essentially a pittance at least as far as business/dressy clothes go. Department store goods and competent restaurants are a dime a dozen in Beijing/China, so there's not much relationship to risk there by bargaining and having to walk away empty-handed.