I wish you had shared more about the details, such as what this "serious personal reason" is, how you found out, the nature and extent of the bullying, and your relationship to the two people involved (relative, coworker, customer, direct report, friend). Regardless, if you are concerned, then you have an ethical and moral duty to speak up and try to stop the bullying from progressing further.
Some companies' policies state that employees must report non-compliance with company policies. Additionally, if you are a member of management and this involves sexual harassment or harassment based on another legally-protected factor, you have an obligation under the law as an agent of the company to report the misconduct. Even if it doesn't involve a legally protected factor, think about what you'd want if you were in the Assistant Manager's shoes.
If the Assistant Manager can't or won't speak up for him or herself, then you can report the misconduct to HR, upper-level management above the GM, or anonymously via a letter, but be specific in your claims. You might tell the Assistant Manager that if they don't report the behavior by (give a date), then you will. (Today the Assistant Manager is the victim, but tomorrow it could be you or anyone else.)
When reporting the issue, describe the offending behavior and when/where it occurs, who is the target, why they are targeted, how long it's gone on, what the impact is to the individual and the group, who knows about it and what has been done (or not). The chances are that this is not the first time this General Manager has been complained about. If this is a safety issue, be sure to highlight that.