This is a bigger issue than I have time to write comprehensively on now, so I'll point you in the direction of a couple of articles which express our position on BDS:
"Why left-wing students should not support boycotts of Israel"
"Why unions should not break links with Histadrut" (not about BDS as such but contains some stuff about our general attitude)
It's worth saying that our attitude to, so to speak, "B, D, and S" and our attitude to "BDS" are not necessarily the same. We are explicitly in favour of, for example, campaigning for Britain and America to stop arming Israel (a form of sanction), and we also support targeted divestment campaigns. We're not enthusiastic about boycotts in general for a whole variety of reasons, but if we were based in Israel I doubt we'd oppose, for example, Gush Shalom's campaigns to boycott settlement goods even if we didn't make them our main focus.
Our issue is more with the way "BDS" has become a kind of political religion in the Palestine solidarity movement (a critique also made, for what it's worth, by former BDS advocate Norman Finkelstein). It is misleading and disorienting on questions of agency, and exceptionalises Israel and Jewish nationalism in a way that can tend towards some very ugly politics.
Anyway, have a read of the articles and let us know what you think.