Producers produce, writers write. You need to establish your credibility if possible in your query letter to assure the producers that it is worth their time to read your script. I don't want my electrician asking me how he should go about getting the job done or asking my assistance answering electrical issues - that's why I hired him. Similarly, producers feel better and have greater confidence in writers and their screenplays if the writers exhibit a firm grasp for their field and what they're writing about.
1. Mention Something You've Had Produced
If you have had a script produced legitimately, that should be placed in the opening of the letter. This is where you can name-drop anything associated with it to legitimize it. This does NOT include a producer saying they "think it's great" but passed on it. They obviously didn't like it enough to option it.
Same goes for when someone options your screenplay. Don't tell a producer that the script you're talking to them about has already been optioned and shopped around town. This will not appeal to them.
However, if you had a different script optioned by a legit producer (not the script you're writing about in this letter), then you can mention that early on as part of your bio. Writing
2. Contests or Awards You've Won
Placing in the Top 5 or 10 of a contest or winning awards also tells the producer a bit of screening has been done on your script and that someone who reads a lot of scripts seem to like it.
However, be careful about mentioning where you placed in contests if you weren't in the Top 10%. If you state that you made it to the quarter-finals and nothing more, that actually detracts from your credibility because there were clearly many more that were better than yours.
Make your award or contest sound the best it can by how you present the accurate statistics. For example, if you placed fourth in the Nicholl Fellowship, you could say you placed fourth, but this reminds us that there were 3 that were definitely better. Instead, state it as a round number and say that you were "In the Top 5." If you know how many entries there were, you could even say "out of x" number of entries.
3. Respected Screenwriting Training and Script Development
When I do a screenplay consultation, the first question I ask my screenwriter is "What is your background and training? How did you learn to write screenplays?"
Their answer gives me an introduction to what I'm going to get when I read their script. The fact is, I've read scripts from writers who completed 2 years of an intensive screenwriting program who still had a long way to go - and I've read scripts from writers who mostly studied on their own and were surprisingly good.
But in a borderline situation with a producer who is not convinced they want to read your script, strong training might help push them over the edge.
If you don't have anything that can give you credibility, then don't put anything, just leave them wondering. It's better not to put anything than to put something that has little value because then they will know, for sure, that you have no better credibility.
So there you have it - three possible ways to enhance your credibility in your query letter bio. Ultimately, your bio needs to move them forward in reading your script and, if possible, to even color their experience positively before they read it.