Thanks Vernon,i have just sent off an enquiry about booking four bikes on each train,so we can i get home together.
It's very likely that the official capacity of the Bridlington to Scarborough train is two bicycles as the service is Northern rail and they don't do bookings and the train is likely to be a pacer with a two bike capacity. The number of bikes is over two that are accepted for carriage is entirely at the discretion of the train guard. You need to practice your charm skills.
The train service from Scarborough to Leeds is operated by Transpennine Express trains using three carriage train sets with a two bike capacity. Booking the cycles on these trains is
essential to guarantee passage through to Leeds. If someone turns up along the line with a booking and your bikes aren't booked on you might get turfed off the train to make room for the booked cycle. The booking can be done online for bicycles. The booking system will not allow more than two bikes to be booked onto the trains. if someone has a bike booked on after Scarborough and before Leeds you will not be able to take advantage of the two bike spaces through to Leeds.
My suggestion is to chance it with the Bridlington to Scarborough train and come back in twos on the 18:50 and the 19:50 trains. The wisest riders will opt for the later train as they can get more beer in before coming home.
There's no alternatives available for the carriage of four bicycles unless you take folding bicycles or take bike bags with you and partially strip the bikes and bag them up whereby they become baggage and not bicycles.
The problem is not restricted to these lines. The two bike limit was a notorious bottleneck for LEJOG cyclists wanting to travel to Wick and Thurso from Inverness and vice versa.