While there isn't a definitive answer, it seems likely Peter has developed his physique through his activities as Spider-Man.
Spider-man's origin in the comics is a little different from what's shown in the Raimi movies. His powers kick in minutes after being bitten by the spider, and seem fully functional immediately:
We see Peter with his shirt off in Amazing Spider-Man (1963) #8:
While Peter doesn't look incredibly puny here, note that he is called "stringbean" by someone who can see him standing there shirtless. Also, it is clear that Flash Thompson does have a more powerful looking body.
So, no, it doesn't appear that the development of Peter's physique occurred purely from the spider bite. Logically, years of swinging around town, jumping, and fighting while using his spider-sense to avoid taking any more damage than necessary lead to further development of his physique, leading to more powerful muscles.
I would be remiss in not noting that a part of this can be attributed to the artists drawing the comic. Clear through his last issue (Amazing Spider-Man (1963) #38), Steve Ditko drew a Peter Parker who looked relatively thin and weak. Here, he doesn't appear to have more bulk than Aunt May!
However, the book's next artist, John Romita, seemed to bulk him up to at least average size almost immediately. In this image from Amazing Spider-Man (1963) #39, Romita's first issue, Peter's upper arm seem larger than the doctor's: