Big guess. I think bleach would be my last choice as it is generally corrosive. But having said that, if it was my only choice, I do not think a one time application would be a problem. BTW, I would follow the directions which is to let it dry. One of the quat products maybe a better choice. You could call Clorox and ask them since they make bleach and quat products.
If you are the only one using the bike and you are the one who is sick, you could cover it after use so no one will touch it. And, if someone does touch the covering, they will need to wash their hands.
Just a side note,if you are sick, I hope you have a plan to not infect the family. I only say this since the bike might be able to follow you to your 'protected' space in which case it will not be touched by others in the house. Sanitation of that space would be less important.
Hoping all turns out well!