Reading glasses can be made for single vision as well as bifocals/progressives, it is decided by the usage. If you just use the reading glasses for reading books and papers, it can be made into sigle vision. If you suffers from far-sightedness or presbyopia as well as near-sightedness or have troubles in viewing computer, then your reading glasses can be made into bifocals/ progressives.
There are many types of reading glasses available on the glasses market like non prescription reading glasses, prescription reading glasses, bifocal reading glasses. So not all reading glasses are bifocals. If you do have more than one vision problem, bifocal reading glasses are need. According to what you said, you only need prescription reading glasses just for reading. With prescription reading glasses, you will see things close-up clearly. Hope this will help you.