So I did test a bit with damage reduction from Zane Skills, Rough Rider and Distributed Denial.
Testing was done on MH3 True Vault Hunter (which might skew results). I was mainly interested in how different DR values work together and if DR from shields (or other passive bonuses) are added to Zane.
As a test I wrote down shield damage without DR from a Skag (lvl 51) and then wrote down damage numbers (all melee, no visible MH bonuses) after changing gear stats.
Base damage: 1624
23% (RR) DR: 1250 ( 76,9%)
23% + Barrier: 1120 (68.9%)
16% DR (SUL): 1359 (83.6%)
15% DR (FB): 1377 (84,7%)
23% + 16% (RR+ SUL): 1046 (64.4%)
23%+16%+Barrier: 938 (57.8%)
16%+15% (SUL+FB): 1181 (72.7%)
16%+15%+23% (SUL+FB+RR): 909 (55.9%)
16%+15%+23% + Barrier: 814 (50.1%)
This shows that Zane clearly does get added DR when near the Barrier (only when Barrier is deployed, carrying it won’t give any DR), which should work for other passive shield addons (e. g. 40% chance to absorb ammo) as well. It could be 50% (things that are skewing results can be MH, TVHM and a level difference of 1).
Also the game does not seem to calculate DR as in Borderlands 2. 1/(1+DR) would give a lot less DR. Those numbers could suggets that and DR is applied multiplicatively ((1-RR)(1-FB)(1-SUL)). Numbers don’t add up perfectly but would be much closer than compared to the old formula (about 1 percentage point difference in most cases), though the difference between observed and expected results is still pretty large when adding more sources of DR (but a Zane bonus of 40-50% might fit with those numbers).