Click on Mariposa Grove under "Winter Trails" for a PDF map:
http://www.nps.gov/yose/planyourvisit/brochures.htm(there's also a summer hiking map, but it doesn't show the closed road to the grove).
Basically you park near the Park's south entrance station, shown on the map, and walk on the road. It's about 4 miles 1 way. Figure it's an all day thing.
It's safe from bears. Meaning, they are there but it's unlikely you will see one or they will bother you.