The only exception to the openness and participation of all governors I so often mention is any process involving an individual which at a later stage might be the subject of an appeal. At the time your governing body elected these three governors as its staff disciplinary committee, it will also have elected at least three different members to serve as an appeal panel. Whatever decision is made, your teacher can appeal against it to these three different governors who are not prejudiced in any way by what they may have heard. That is the fairness which this process is designed to safeguard.
We have to trust our fellow governors in matters like this, having elected them to do a job on our behalf. They will have been briefed on how careful they must be in procedures and principles of natural justice, and warned about the possibility of an appeal to an industrial tribunal. The head will also be involved.
So I should not worry about the outcome unduly. I would think it extremely unlikely these days that a good and otherwise blameless teacher would be dismissed for being in the wrong bed, if that is the problem (as you fear), unless the liaison and the circumstances were such as to damage the school, through conspicuous indiscretion, bad publicity, or distress to ex-partners or children within the school.
Finally, if the worst happens, she can appeal. A more complex question to which I've never had a straight answer is whether the main facts of the case should be made known to other governors if and when the period for an appeal has expired and there is no appeal, or when the committee accepts that the offence took place but the sanction stops short of dismissal. Almost any teacher would say no and almost any governor would say yes.
In my experience, governors are not given any information. The principle involved is whether there is "need to know". Governors might, for instance, be considering the teacher for a promotion to a post where the nature of the offence was particularly relevant.
On the other hand, isn't any resulting prejudice double punishment? Can't we trust the head to take appropriate account?
Incidentally, the Government proposed that governors should only be involved if there is an appeal, and otherwise it should be for the head to dismiss. This provoked many objections and is to be considered further.