Some shops do special plastic bun snappy hair ties, all you have to do is clamp them round your bun and apparently it snaps into place. Ask at local beauty/hair shops, I used to have one but never tried it!
If you hold in a ponytail and twist the hair quite tight before making it into a bun shape that helps hold the ends in. Hair pins (as opposed to grips) are great for holding tiny wisps of hair and don't show up much. Otherwise I'd recommend misting with hairspray and then instantly smoothing the hair with your hands so that it sticks down properly.
I can wear my hair in a bun too. All I do is while its still damp, fasten it into a ponytail and then twist it round until you can wrap it around. To secure it I use a fabric scrunchie which keeps everything neat and tidy.