The Mersey Beat. It’s a pattern that’s currently missing in the BIAB drum repertoire. But be aware that it can vary quite a bit, but for ‘From Me to You’ (and ‘Dr Robert’)
Ringo uses the following drum pattern in one bar that is repeated with some additional fills:

Eight taps on the cymbal
A hit of the snare on the first tap and seventh tap
And a hit on the bass drum on the first tap; a half time hit on the fourth tap and a full time hit on the fifth tap.

The best way to implement this is to use a Sequencer/DAW (e.g. Sonar, Reaper or Real Band) using for example EZ Drummer or equivalent to program the drum pattern and transfer as required other sound tracks based on the chords generated by BIAB.

If you need to get the detail drum patterns get the entire music scores:

The BEATLES Complete Scores by Hal Leonard Corp. ISBN 0-7935-1832-6 1993.

It has musical notation parts for all instruments used in all their songs.

(Tip: If you get into the Beatles style as I have, getting hold of the EW ‘Fab Four’ sound library is a good move as it contains many of the exact original instrument sounds used by them.)