It only appears during the Bug Catching Contest in National Park, which is held once a day on Tuesdays, Thursdays, and Saturdays. And it turns up all times of day during the contest.
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There is nowhere the player can capture a wild Bulbasaur in Pokemon Crystal. It can be traded using the Time Capsule.
Go to the underground entrance near Bill's house in Goldenrod City. The haircut brothers appear everyday, besides Mondays, in real time.
You can't make time go faster, but if you want to make the play time continue, leave the game on during in a middle of a task. Pokemon Crystal is based on in-life time. Whatever time it is in real life, that's the same for Pokemon Crystal, unless you had set it to a different time than yours.
You can get Misdreavus in the Silver Cave at night time in Pokémon Crystal.
Happiny did not exist at the time of Pokémon Crystal. Therefore, it cannot be obtained.