What I intend to present here is a series of templates and principles that should make the task take under five minutes and be a relatively low stress endeavor.
The purpose of the bio is to let the audience (including other industry professionals) know a bit of additional relevant information about you. While to some degree it can serve to establish the credibility of the artistic team, if you are early in your career (or even doing your first show) that is also an interesting bit of information to an audience. (With that in mind please realize that no one worth knowing is going to judge you harshly for being new to the field, so don't worry about having a short bio.)
This post is particularly aimed at people early in their careers. Remember that you'll be getting more credits as you go, which means that your bio can change constantly throughout a season.
These are all fairly flexible and geared for short bios. Long-form bios are basically expansions on the template. (I have bios for several of the disciplines I work in throughout my site).