First let me say that I played the entire open beta/head start and yes, I know how to assign a bridge officer. However, I've lost 5-6 once head start got going and thought I'd lost a blue one last night before I tried something that got it back for me!
Here's what happened, step by step.
1. I finished a mission and saw a text that New Bridge Officer mission complete.
2. I stayed in within the system and did NOT exit to sector space.
3. I was only offered one officer, so I check the circle and then hit accept and join rather than train up.
4. Staying in system space, I checked my assignments and of course, no BO there.
5. I complained to my fleetmates that I just lost another!
6. I noticed that the New Bridge Officer mission was still listed on the right hand side of the U/I where missions be default show up.
7. I decided to "re-try" and hailed Starfleet and immediately noticed that the mission was still offered even though there was a check mark next to it.
8. I clicked on it and talked to the Starfleet Bridge Officer Assignment lady (can't remember her name) and after talking to her, I got the "bridge officer awarded" or whatver that message is.
9. Went back to the assignments tab and voila, there's my bridge officer!
Possible reasons why this worked:
1. sheer chance
2. BO awards are bugged and the steps of getting the award have to be followed in a certain sequence.
I believe that the steps the player takes in accepting the award have something to do with this bug. The fact that it was not in my assignments tab the first time, but was the second time, is a sure sign of that. I read a post on a thread elsewhere from someone who stated that they also did something similar to me and had the BO show up, so please, try this before you give up!