In season the train is extortionately expensive. Not sure about this time of year. Driving is much more convenient and you can take your bike but I would advise against riding Sat and then driving the 5+ hours back – very tiring. We’ve done a weekends hiking driving up Thur evening, all day hike Fri and Sat then breakfast / scenic drive to start trip home on Sunday. If you’re going up you want to hit some signature rides eg Helvelyn, Borrowdale Bash plus say a loop round Grizedale area. Not sure how fit you are but a drive and two mega all day rides and a drive back will be knackerinf and possibly unsafe in the car on your own
The Lakes are fantastic but if you want a weekend you might like to consider a “dry run” trip the the Peak District as that’s 3.5hr drive instead of 5.5hrs – I’ve done that solo driving with 2 days riding a number of times