One of the most stereotypical cases of bullying is to be openly mocked and made fun of in front of your peers for a perceived difference. There's no violence involved in that.

Have a look at what constitutes bullying [0]

Violence is but a subset of it.

Unless we were to water down the definition of violence to include any manner of ridicule. At which, you're diluting the definition of violence under the guise of staying steadfast on the definition of bullying necessarily including violence.

[0] http://www2.gov.bc.ca/myhr/article.page?ContentID=44eaf3f0-f...