Can you pick up herpes on your hands from touching things, and contract it genitaly when going o the bathroom?

No risk, no worry. Nobody ever catches herpes by contact with surfaces, or by sharing bathrooms, toilets, kitchens, eating utensils, etc. The virus is only transmitted by direct contact with another person's infected area, such as genital area or lips. Don't worry at all about this, even if you are sharing a toilet with someone known to have genital or oral herpes.
No. Although, there might be anecdotal presentations, the one you are describing sounds impossible. First off, to spread herpes, there must be a certain concentration of the virus. When you touched a thing, i highly doubt it has a significant concentration of the virus on it, as it doesn't like inanimate objects, secondly it must multiply to reach a critical mass to become contagious.