There are quite a few busses from Camberley Surrey that cross into Hampshire or Berkshire, like ones to Blackwater, Wokingham, Bracknell, Aldershot and Farnborough
A full journey on the Stagecoach 18 from Aldershot to Haslemere crosses the Hants/Surrey border three times as it makes its way from Aldershot (Hampshire) via Farnham (Surrey) and Bordon (Hampshire) to Haslemere (Surrey).
I've tried to make a list of all the services that leave Kent (ignoring services which cross between Kent and Medway). I've ignored a couple of very infrequent services, but I still have:
2 (Stagecoach) - Tenterden to Hastings (East Sussex)
28, 29 (Brighton and Hove) - Tunbridge Wells to Brighton (Brighton and Hove)
96, 428, 492 (TfL) - Dartford to Bexleyheath (London) and beyond
100, 101 (Stagecoach) - Lydd to Hastings (East Sussex) via Rye
228, 229 (Compass) - Tunbridge Wells to Crowborough (East Sussex)
231, 233 (Metrobus) - Edenbridge to Lingfield (Surrey)
233 (TfL) - Swanley to Eltham (London)
236 (Southdown) - East Grinstead (West Sussex) to Oxted (Surrey) via Edenbridge
246 (TfL) - Westerham to Bromley (London)
251, 252 (Stagecoach) - Tunbridge Wells to Heathfield (East Sussex)
254 (Stagecoach) - Tunbridge Wells to Hawkhurst via Wadhurst (East Sussex)
256 (Autocar) - Tunbridge Wells to Wadhurst (East Sussex) via Frant (East Sussex) and Lamberhurst, crosses the border three times
291 (Metrobus) - Tunbridge Wells to Crawley (West Sussex)
304, 305 (Stagecoach) - Hawkhurst to Hastings (East Sussex) via Robertsbridge
312 (Stagecoach) - Tenterden to Rye (East Sussex)
349 (Stagecoach) - Hawkhurst to Hastings (East Sussex) via Bodiam
431 (Go-Coach) - Sevenoaks to Orpington (London)
477 (Arriva) - Swanley to Orpington (London)
594, 595 (Southdown) - Westerham to Oxted (Surrey)
B12 (TfL) - Joydens Wood to Bexleyheath (London)
R5, R10 (TfL) - Knockholt Pound to Orpington (London)
X80 (Ensign) - Bluewater to Lakeside (Thurrock)