Well if you go with the literal interpretation of the song your magic bottle would let you "charge" the bottle by spending days which the PC basicly skips...the PC wakes up in the morning, pops the cork, says an activation phrase for the bottle, including how many days he wants to save ie: "Into this bottle i shall save the time remaining of this day, and forward hence another three, to share with my beloved lady". Which in effect saves 4 days upon the successful arcana check, thereapon the character, thrust those four days forward in time can go on about his business, with other people wondering where he was for those days.
If the arcana check fails no effect takes place, if the roll is a crit fail there is a backlash whereupon there can be a few different outcomes, like many more days (multiply by 1d6+1 days that are actually saved) or possiblly the character is thrust back in time the 4 days and has to "re-live" those days. As a twist if he was adventuring those 4 days previous he pops up wearing his sleeping clothes wherever he was...in the middle of a battle perhaps? Of course his gear would be there (it was with him originally) it just appears he stepped out of his armor, or adventure clothes or whatever..
To use the charged bottle the PC needs to be in a safe area, holding hands or otherwise touching who he wants to spend the time with (or alone and ready to seek out the person in question and hope they were not busy), pop the cork and bingo he is back in time for the time period he saved. At the end of the time period saved he and his companion pop forward to just a moment after they went back. Anything aquired and either carried with them or placed in a secure location would still be with them/there. Could be really handy on a dungeon crawl because if you phrase it right you can save your time and place ie: In this place and at this time i wish to save days numbering 4, to resupply and mend our wounds and then return through times trap door. Of course all party members should be there at the time the bottle is charged so noone gets left behind (if they don't have the time saved they can't go back...paradox and all that).
Seems to be artifact level magic to me, or at least unique item with a limited number of uses, say 1d6 or more if the gm is generous afterwhich the bottle breaks and is no longer useable.
Also as good RP make the character(s) actually use a rhyming phrase for activating the timesaving bottle, makes them think on their feet and use teamwork toward their goal.
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