Why not grab a cab from your doorstep to Lulworth and potentially save money on trains, buses etc. especially if you share with friends. You can even book to get picked up at the Drop-Off/Pick-Up point at White Gate and get dropped back to your home.
There are also special rates for 7 seater cabs with plenty of space to carry camping gear. This could be the perfect way to enjoy the weekend and have someone pick you up from your door and take you back home again.
Visit minicabit.com for a cheaper, easier deal.