There are many ways to say sorry to someone. This is expressed when someone feels regretful or sorry of something done to someone else (Althought the deed is done unexpectedly).
Some of them are;
I am sorry
I am so sorry
I am awfully sorry
I am terribly sorry
I am very sorry
Please forgive me
I do apologize
The adverb of quality "so" here, is to stress the feeling of apology.
You also can say : "Sorry ..." without subject and the verb.
In Formal situation, you also can say;