If you're in search of cheap sheets for your bed that are cooling and hypoallergenic, look no further than bamboo sheets.
The cheapest price you're probably going to find online for these is around $20 a set. They won't be great quality sheets, but you'll end up with something that works for a while until you can get the better, more expensive kind that will last longer. These are usually off brands that you're likely to only hear of a few times and then they'll be gone. This is indicative of some "fly by night" companies that come and go on a regular basis. They'll find a supplier of cheap bamboo sheets out of China or India, slap their label on them, and sell them online, either on their own website or somewhere like Walmart.com.
Mid range, you're looking at around $40 to $80 per set. These are a lot better and will last a while. Just don't expect them to last decades like high quality cotton sheets will. Natural fibers will always be better than synthetics. But, bamboo sheets made of semi-synthetic fibers; we say "semi-synthetic" because the fibers are made of chemically treated bamboo cellulose.
Top of the line bamboo sheets will run you $100 to $250 per set. Cariloha makes great high end bamboo sheet sets and has been around for a bit. They also make other bedding products such as pillow cases, duvet covers, and even mattresses.