It's exactly as written in Jay's answer. Not only that the so is not informal, but also is written perfectly correctly.
What bothers me is the therefore. It's indeed formal, but it's not written correctly.
You should write it like this:
My experiences are non-traditional. Therefore, I am wondering what to do about/with my application. Now, my answer is ...
See, I put a comma (
,) there (after the word therefore). To write a consequence sentence after the cause sentence, you write the word connecting them along with a comma.
Besides, you are wondering at the moment, so using a past perfect tense is not a good idea. Since it'll mean that you did wonder, not anymore. [This counts only if I get your meaning correctly, that you're still confused about what to do with the application.]
The last thing is, the bring for my application just seems a bit weird and uncommon to me. Cause the verb bring has a direct object. Therefore, it cannot be followed by for (should be followed by a noun). Besides, you can't bring anything if it's about an application. Cause what you bring is the application itself. Maybe you wanted to say:
- what to do about the application, or
- what to put on the application (like what J.R.'s comment said), or
- what to use for the application.
Unless, you meant you're confused what application to bring.
On the other side, I prefer therefore, cause it'll make the sentences look pretty well arranged. [What you were confused might not be the informality, but the "look" of the sentences]
This is a better formed sentence suggested by Damkerng T.:
I am well aware that my experiences are non-traditional at best; therefore, I am wondering which experiences of mine are worth mentioning in my application ...