***** NOT A TEACHER *****
IF (a big "if") I understand my books, you do NOT "need" to say / write "I."
Look at this sentence from a very respected guide to correct English * :
"We fished all day, but (we) didn't catch a thing."
As you know, when a word is put in parentheses, that means that the word is optional. In formal speaking or writing, it would probably be a very good idea to repeat the subject "we."
So -- in my opinion -- your sentence is acceptable in ordinary speech and writing:
"(I am) sorry to ask so much, but (I) hope (that) someone can help me."
* L.G. Alexander, Longman English Grammar (1988), page 10.
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