The Haste from Drakk’s max-band is permanent, so that Bombaster will have Haste until it leaves play. This matters if your opponent plays Wandering Mimic or steals Bombaster using Mind Control or Ogre Recruiter.
The Haste from Drakk’s max-band is not copied by copy effects. Here is a comprehensive list of things copied by copy effects:
- The stuff printed on the card (including color, types, abilities, atk, hp, tech level, cost, and probably some other stuff I forgot, but not including whether a thing is a token or not)
- Other copy effects
- Polymorph: Squirrel
- Atk values set by Chaos Mirror
This is maybe a little arbitrary but it basically works the same as some much older game’s copy effects