Will Ash ever meet Ho-oh in the anime face to face?
Possibly, especially since he saw it early n Kanto, but we can only speculate.
Why doesn't ash catch any legendary pokemon he sees?
Many of the legendary pokemon serve a purpose like
protecting areas and keeping peace. If
Ash were to catch them, that would
disrupt the ecosystem. The show would
also be very boring with Ash carrying
around a legendary everywhere. There
would be no challenge, and there would
be no reason to watch it. Also, if Ash
had a legendary pokemon, what's to
stop Team rocket/plasma/etc from
ganging up on him and stealing it? You
really think giovanni is gonna
overlook that? Even if they fail,
they're just gonna keep trying, making
for an even more bland show.
Compliments of the Anime FAQ
Why does it keep showing itself to Ash?
We don't know what gamefreak is thinking, but Ho-oh's pokedex entry says that lt will reveal itself before a pure-hearted trainer by shining its bright rainbow-colored wings, so it likely considers Ash a good trainer. He never actually reveals himself to Ash, he's just spotted by him in the distance.