I’m arriving in Taipei for 6 weeks of research work - I’ll be staying at an international student dorm that pretty much only supplies a “Chinese/Taiwanese” bed - just a hard plank supported off the floor.
Where would I find affordable “bedding” appropriate for a university dorm? Hopefully affordable in the range of “I won’t feel bad about leaving it behind / giving it away / etc”. (The students I’ve spoken with weren’t much help - Mom and Dad usually procured everything for them…) 
For just six weeks, you could put down a yoga mat then a sleeping bag; these should be available (and cheap) at places like Carrefour, RTMart etc.; there are also bedding stores in many traditional neighborhoods – just look for storefronts with pillows, mattresses etc. Ikea has cheap stuff too.
bed sheets… there is usually someone selling horrible quality bedding sheets at the night markets.
I’ve seen Costco prices for about the same as IKEA for the whole set together (even including the flat sheet which is harder to find here).
I vote for IKEA. I slept in one of their thinnest mattress, the one that can be rolled, at that time was like about 2 thousand -you can take it home by taxi- for almost two years, no problem, confy. And I had a bare wood plank underneath. I would suggest investing in a better quality pillow, and bring your own bed sheets and stuff -as said, used and nothing to worry about to leave behind. Night market ones have too many chemicals for your health, good ones a bit pricey, unless on occassional sales.
True. If you have membership elsewhere, though, it works here too.
IKEA. Bedroll, sheets, pillows all in one place. Located in the city, too. 