There are few simple rules that you can easly follow so as to ease the process of making reservations:
First: It is a good idea to know what type of apartment you are looking for. Do you need a two-bedroom or a small studio.
Second: How long are you going you stay in the apartment? The longer you stay the better deal you can get.
Third: What location is going to be more suitable for you. In the city center you are going to be within 15 min walk to almost all of Sofia's landmarks and institutions. If you choose to stay near the center or even in the suburbs you are going to be in a more quieter atmosphere.
Fourth: What price are you ready to pay? If you have a pre set range that you are willing to spend you might have to make a compromise with your demands in order to not to exceed to limit.