This is a common way to ask for information.
I would interpret it as an elision of "I was wondering earlier", and I'd say that the reason it's preferred to "I am wondering" is that it sounds less direct. "I was wondering" only implies that he would like to know now, whereas "I am wondering" is closer to an explicit question.
It is common in English to state things in a more indirect way to be more polite or deferential, for example "could you please do X" is softer than "please do X" and the former is more common in conversation.
In this case, Sheldon is appealing to an authority figure, his father, about something that he knows is likely to be met with disapproval, so he's likely to subconsciously choose a meeker tone. Interestingly, Sheldon as a character is exactly the sort of person not to understand the social nuance of the word choice, but "I was wondering" is much more common and so he'd likely choose it by default as the normal way to ask.
Looking at Google Ngram for the two, "I am wondering" peaked in usage in the 1940s and has been declining rapidly since, whereas "I was wondering" has been increasing in frequency rapidly since 1990.