I'm pretty sure the shot of Bag End included the "no admittance except on party business" sign on the gate, plus Holm's vocal performance is clearly the "well preserved" Bilbo and not the rapidly ageing one from the end of RotK. I think it's safe to say the framing story takes place immediately before 'Fellowship' starts.
Oddly enough, it actually fits into the canon of the story better than one might expect. Remember that Tolkien re-wrote how Bilbo got the ring in later printings to bring things in-line with LotR and that he accounted for the discrepancy by saying that Bilbo (already under the ring's influence) lied about the exact circumstances. Only much later (just prior to LotR) did he admit the truth and amend the account in his book. Though if memory serves, it was Gandalf that got the truth out of him, not Frodo.