The other option is to get some faction armor for the Brotherhood.If you've done (or are in the process of doing) her loyalty quest, though, these paladins might be part of that. There's a pretty good chance that she'll be able to get you into the bunker. If you can, head to the 188 Trading Post and pick up Veronica who is from the bunker and can be relatively easily convinced to take you there.There's a couple of reasonably surefire ways of getting into the bunker without violence, though: One important note is that if you tend to wear NCR armor, don't, as the Brotherhood is hostile towards NCR.
The problem is hard to pinpoint, since the game's scripts are very complex and there are more than a few bugs. There's no faction impact for doing ED-E's quest line, so that's not your problem.