From time to time there are cases when I would really like someone else to blow their nose, whether it be because they're constantly sniffling, or that I can see snot in their nose. Neither of those are nice things, so I really want them to blow their nose. Is there any way of hinting at them to blow their nose? Or a certain way I could use to ask them to blow it? This situation usually occurring around other friends/people too, so I don't want to say/do something that would place them in an awkward situation around other people.
Assuming that person is a friend/acquaintance (as stated per OP's comment) I would consider it not particularly rude to offer a Kleenex (uhm, mint condition, obviously). Any reasonable person should catch the drift. Since said person is a friend/acquaintance you should be able to tell how they would react to the offer. If they, however, reject the offer it would be somewhat impolite to insist and make additional remarks on the topic.
If the person is a stranger that just happen to share the bus with you, well, minding your own business is probably the best way to go.