The only legal routes into Tibet are: 

1. Via Chungdu where you can buy an air ticket for 3000Yuan ($375) This allows you to travel around Lhasa.

2. Via the Golmud to Lhasa highway. From this remote town on the borders of Qinghai and XinJiang there is a 35 hour bus route to Lhasa. Although there are stories of successful attempts without paying the permit fee 1750 Yuan most people have to pay. 

3. Nepal border. The days of crossing from Nepal to Tibet with no restrictions are gone. Although it is possible to cross into Zhangmu (the border town ) from there you will need a permit to travel to Lhasa which you can only obtain by organising a tour which will include a truck and a guide. This will set you back about 1000yuan. If coming on a bike all these entail putting your bike on the roof or cargo hold of thr transport you’ll be forced to take and riding out from Lhasa mot to it.

4. From China into Lhasa; it is possible to take any of the routes into Tibet if you are willing to fork out the dosh!
As a cyclist you’ll have to give exact days of travel and a detailed itinerary.
Paying for a jeep tour with transport and guide I was quoted $3000 for the Yunnan route. 
Peter Stewart of Himalaya mountain bikes based in Katmandu can help you organise the permits although he would need a considerable amount of time to get it organised.
 From Deqin on the border in Yunnan a travel agent offers a 6 day jeep tour for 17500yuan. 
In Hong Kong there is a travel agent that offered the bike tour for $3000US. You can get in touch from the Chinese Embassy in Hong Kong.