[BSPeter]

No special setting required except selection of "Auto play" (=2nd option) under
(rightclick >) Options > Preferences > General [General settings]

Originally Posted by BSPeter

To put correctly named ascending files, like abc1.avi abc2.avi abc3.avi abc4.avi abc5.avi in playlist to play them sequentially, there is no need whatsoever to select "Always add all files in current directory to playlist".
If - with this option deselected - you load/play the first file of a sequence, the following files will be added automatically in playlist.
E.g. if you load abc1.avi: all files abc2 to 5 will also be added to playlist and abc1.avi is ready to play or starts to play (may depend on other settings).
However, if you load abc3.avi, only abc4.avi and abc5.avi will be added automatically (with abc3.avi starting to play or ready to play).
Further, you can also make BS.Player "remember" where you left last time (also in the middle of some movie), by setting "Remember last movie position" under General Preferences. Next time BS.Player will ask you if you want to continue from the point where you left.

Note to be 100% sure I just tested with BS.PlayerPro 253 1034 using 2 files:
Mongol.2007.DVDRip.XviD.CD1-TDM.avi and Mongol.2007.DVDRip.XviD.CD2-TDM.avi !
(I only selected the CD1-file; the CD2 file was automatically added and played.)