You can alsodo this with motorcycles, computers at some shops and most large purchases in Taiwan, not just apartments.
Bargaining is a way of life on Taiwan and at some point, you should try to do it on your own. It'll sharpen your negotiating skills and you'll get a better understanding of business on the island. Although, there's nothing wrong with calling in Chinese support too. Its works even better when you 2v1 somebody.
Last apartment I had I saved NT$3000 on the monthly rent and took the deposit down to one month. My motorcycle went that way too.
Of course, each person on Taiwan is different, so there will be different levels of acceptance when it comes to bargaining. But, I think if you don't do it, then they'll think you're another ben ben de wai gwo ren.
Salary also can easily go up, when you negotiate as well.
The most basic strategy is pointing out the deficiencies of something you want to purchase to get that price down, and pointing out the positives when you want to start out with a bigger salary. Try to be willing to lose what you're buying (you can always go to the next place) and don't promise too much when you're selling (otherwise you get your self in hot water when they find you can't deliver). By doing this, you'll be able to see your income go up 10 to 20% and your expenses go down another 10 to 20%.
If you feel uncomfortable in bargaining, just call in a Chinese friend, and then you can also listen him/her to know how to do it the next time.