Can I do union organizing while I'm at work?
You have the legal right to engage in union activity on the job on the same basis as any other non-work activity. You have the right to do union organizing before and after work hours, and on break time, away from work areas.
What about distributing union literature at work?
The same principle applies: the rules have to be the same for union materials as for any other non-work-related literature. If you're allowed to pass out information about a church picnic or sell candy for your kid's fund-raiser, then you have the right to distribute union literature. If your employer bars all "distribution on company property," then that applies to union literature, the same as any other materials.
What about the company bulletin boards?
The simple rule is, once again, that union materials and activity shouldn't be treated differently from other non-work-related materials and activity. If you can post non-work-related notices on the bulletin board, you have the legal right to post union materials.