And here, of course, we get REALLY murky, as the "...Revised Calendar developed by Mardil was called Steward's Reckoning and was adopted eventually by most of the users of the Westron language, except the Hobbits. The months were all 30 days, and 2 days outside the months were introduced: 1 between the third and four months [an actual Tolkien typo here, unless it was customary to not say "fourth"!], and 1 between the ninth and tenth (September, October [or Halimath and Winterfilth as known in The Shire])."Leap years? In the Steward's Reckoning? Tut tut, HB...
I can't believe you haven't read and are intimate with Appendix D!...
[Bracketed comments inserted by me!]
Bilbo, therefore, would have needed the wisdom of Manwe to succeed in arriving at the same day/date, as the Hobbits were still on King's Reckoning, with Lithedays, Overlithe, the day that belonged to no week and other such complications. Reconciling this date in either Reckoning should have been no problem for you, HB; you have a computer!
And, before I forget, a very Happy Easter to all my Tolkien Trivia brethren (sistren?); may the Easter Bunny leave you all Beorning Honey Eggs.