yes bathing is not contraindicated and will not spread the infection to other areas. while it would be highly unlikely for a herpes infection to remain in bathtub it would be good to clean and sanitize the tub for the next person. take a bit of caution with drying off. a towel can be quite abrasive to this sensitive area so consider air-drying or using a warm setting on a blow dryer instead of contaminating a towel. the virus can remain on certain surfaces especially damp ones for a short period of time so a bit of caution is needed. hopefully you are taking a good anti-viral medication to treat this condition and limit future outbreaks.
can you take a bath with hsv-2?