Is bulimia only when you throw up your food, or can it be with laxatives too?

Refers to vomiting. Although both bulimia and laxative use are a form of purgatives, self induced vomiting is called bulimia, while laxative use is considered part of the binge/purge cycle. Btw, excessive exercise fits into the "purge" category too.
Both In Diagnosis. The official diagnosis of bulimia refers to any type of binge-purge cycle. This includes self-induced vomiting as well as the use of laxatives or other types of purging behaviors. So, excessive laxative use along with binge eating could mean that a person has problems with bulimia.