The MACMILLAN DICTIONARY says 'gulp' means 'to make a noise as you swallow air because you are surprised, excited, or afraid'.
Not a teacher.
Interested in Language
2. [intransitive] to swallow suddenly because you are surprised or nervous:
I gulped when I saw the bill.
Does that imply that the speaker gulped something that s/he had chewed, or it could be, say, some saliva?
Matthew said it. In the example you gave the person saw a bill that was higher than he expected, so he was shocked.
Way to go, Matthew!