I am playing a character with a stutter in a play. How can I do this convincingly?

I am playing a character with a stutter in a play. How can I do this convincingly? I've been researching stuttering, watching documentaries, and reading about people who have stutters. I see how their physicality changes when they stutter. Sometimes I see people repeat one letter over and over (b..b.b.b.b..bottom). Other times I see them pause then say the word (b........bottom), and it comes out really fast. The play is Ma Rainey's Black Bottom. I am playing a character who suffers from stuttering and is giving the introduction to a song for a band. He is stressed because it's his first time, and he knows he'll probably screw it up. In no way do i want to make it comical. I just want to play the character honestly and understand how it feels. Thanks UPDATE: You all have been really helpful. This has given me a lot of help with developing this character and i'm still discovering new things everyday as i do the play. Here are some pictures of the play and me at this link http://www.laduenews.com/diversions/arts-entertainment/ma-rainey-s-black-bottom-theater-review/article_e0fcb900-8807-11e1-a248-001a4bcf6878.html I am wearing the green suit