From days gone by;
505, 506 Newcastle - Edinburgh via Berwick; 5 hours+ each way, 5 services a day
508 Newcastle - Edinburgh via Jedburgh, around 5 hours each way, 3 services a day
510 Newcastle - Edinburgh via Kelso, around 5 hours each way, 3 services a day
515 Whitley Bay - Glasgow via Jedburgh, Galashiels and Peebles, around 7 hours each way, up to 2 services a day.

I remember taking the 505 to Edinburgh with my parents and the bus was pay as you enter, just a normal service bus.