Again.... they will be absolutely loads of these, past and present.
For instance....
Lightwater Valley is currently served by the 159 (as
@Pyewipecarshed notes) but at other times, was served in the 1990s by United X96/X97/X98 and 146/161
Alton Towers - D&G X41 and 32A but also had the 14, 15, X52, and X39 IIRC in the past
Amtree Park was served by the UAS/EY121 in its short existence
Great Yarmouth Pleasure Beach is served by the 1C, 2, 3 and 3B
Drayton Manor used to have an Arriva service but not now
Longleat isn't really served though the 53 does serve Picket Post roundabout - good walk to the entrance, brisker walk if you're doing the Safari Park!
Legoland - 701/2/3 but think it had a dedicated First service (200?)
Paultons Park - served by the X7/X7R
Blackgang Chine - served by the 6
Milky Way - served by Go Cornwall 319
none of the
Gullivers have a reasonable bus link AFAIK
American Adventure - was served by Trent 120/248 when it was around
Flamingoland - YC 840 but was the 92 in the past
Spanish City - most routes from Blyth into Whitley Bay
Crealy - Stagecoach SW 9 and 58
Wicksteed Park - Stagecoach 2, 16, 48, 50
Oakwood - Was served by Silcox/Taf Valley 322