In order to improve strength to increase overall speed on the bike, does one need to do weight work or can this be done just on the bike alone by riding? Any best workout plans? Thanks.

Sure. Weight work is a must. Example-I was the fastest in my life just after my army. That was the best shape i have ever reached. Food, resting/sleep and hard training with surgical precision. Comparing to those days, now i am more like a grandma
Regarding your question about workout my advise would be-find the best way, your way, size and scope and type of training. Best quidelines you may find on interenet, of course.
I used I and I still use strength factor training (divide total weight with minutes and you will get factor: pounds/minute or ks/minute. for example if you can push and pull 6t in 60 minutes then your factor is 100 kg/min). High intensity, no more than 60 minutes.

I hope it helped

Adding weights is definately a good idea. Working on my core, doing deadlifts, etc has completely changed my mountain biking. I have much better balance, feel alot healthier, and alot more in control of my bike. Also helps if you need to bail alot - good balance = landing on your feet and not landing on your face (most of the time)