Presuming this is closed source? Although it looks like a neat concept, it would be a more attractive option if I knew something that was dealing with my browsing history was open source.
But FWIW, I can promise you I don't transfer your browsing history. My policy on such data is I simply don't want to ever have a copy of it. If that means I can't sync your history between Link Bubble installs, so be it.
I find it a bit surprising that Chrome doesn't have something similar (or is the relevant sync code just too buried in Chromium?).