Put the cable under your bartape, (option B) that is how is supposed to be done.
Bar end shifters are actually designed to run under the bar tape for a short length along the bottom of the drop.
Not to be run all the way along the bars (you'll probably find the outer supplied isn't long enough for this). You can probably get away with it (definitely with friction) but shifting won't be as crisp.
I run mine with the outers completely outside of the bar tape, makes little difference to me and I can change cables without removing tape. When I've got a bag or stuff on my rack the cables just tend to get pushed out of the way.
Bar end shifters are actually designed to run under the bar tape for a short length along the bottom of the drop.
Not to be run all the way along the bars (you'll probably find the outer supplied isn't long enough for this). You can probably get away with it (definitely with friction) but shifting won't be as crisp.
I run mine with the outers completely outside of the bar tape, makes little difference to me and I can change cables without removing tape. When I've got a bag or stuff on my rack the cables just tend to get pushed out of the way.