Even though you said "don't say it," Networking is your best bet. Figure out what sort of job you want/place you want to work, and find an alum from your school that goes there, and try to meet them for coffee or offer to take them out to lunch. Ask them how they got into what they're doing, and ask for advice for your situation (3L job search) and what they recommend for a course of action. Additionally, by making contacts, when you are actually looking for a job (for example, if you do have to wait until you pass teh bar), you'll have a broader range of people to turn to for some help.
And go back to your career services office to ask for clarification on the bar thing. Depending on what kind of job you're looking for (non-profit, DA, etc.) it sounds about right htat you have to take and pass the bar before they'll consider hiring you - they don't have the resources to hire you on for 3-4 months while you wait for your bar results.