’Bump into’ means to meet someone unexpectedly and is definitely used with people. Another alternative is ’run into’. Example: Can you guess who I bumped into during our stay in the Continental Resort hotel in Sharm El-Sheikh?
As for ’come across’, it is a bit controversial. It is said that ‘come across’ can be used with people, in particular, with unacquainted people. However, as a rule, this term is used with objects and animals. Another alternative is ’stumble upon/on’. Example: As he was reading an English article, he was coming across lots of sophisticated terms which he wasn’t familiar with.