No, it isn't correct: "biglietto" can be a note, a card or a ticket, nothing else.
the bill is "conto" or "fattura", the little piece of paper where bill is written could be named "scontrino"
"biglietto" could mean "banknote" but just if it is specified the value of the bill ("un biglietto da 10 euro") and it isn't very used.
In this sentence, for an italian, "biglietto" is a ticket or, at least, a card.
It hasn't happened yet so it is in the future but at that future period being talked it will be in the past (perfect tense). "I haven't walked across the country yet but when I finish I will have worn out my shoes."
But don't forget that this Italian tense has the other possible meaning of a conjecture about the past. In other words even though it seems like a future tense, the meaning could be "must have" in the past. Someone is surpised to hear that you walked across the country and says "You must have worn out your shoes." using the same form in Italian.
(The same form used to exist in English too: "You will have worn out your shoes" used to have the possible meaning "You must have worn out your shoes." but that form is quite out of date now.)