"It is my bag."
Translation:Es mi bolsa.
Yes, both words exist.
Bolso is normally referred to a hand bag, generally those carried by women, but also men bags and the like.
Bolsa applies to those flimsy bags made out of a unique layer of polyethylene molecules that will tear your hands in 10 mins, garbage bags and mainly plastic and grocery bags.
When referring to holdalls, gym bags, laptop bags, both are almost interchangeable, but they are identified (la bolsa del gimnasio,el bolso del ordenador, ...)
Backpack is Mochila though, although it might also be referred as bolsa o bolso sometimes
Beware there might be localisms out there... whilst this is true, it might not be the whole ;)