The 300 was one of them routes that changed soooo many times. The current 310 is currently the closest representation to it today between Newcastle and North Shields (although it did used to go to Hadrian Park).

https://flic.kr/p/24Hbhtu
Photo of Trident 3867 on the 300 in 2005, a route similar to the current 310 apart from the loop around Hadrian Park, plus it now leaves Haymarket quicker. The location where the photo is now is where Eldon Square Bus Station now stands.