If you have a bit of an adventurous spirit this is the way to go!!!

The risk if you're caught is a fine of up to 2500 Yuan, that's the most I've heard of. Three hundred dollars for the adventure of your life is pretty cheap if you ask me!
Most police don't know the rules, only in a town will they know to stop you. There is a red book with all the rules in it for foreigners in restricted areas and the fine is, for minor misdemeanors like this, up to 500 Yuan or 15 days detained. 
Always bargain on the 'up to' meaning zero be polite but firm and apologize, but refuse to pay unless they threaten you with the 15 days. 

How 
When traveling illegally in Tibet it is important to stay away from the county capital towns. You cannot stay in hotels or hostels as the police will come and question you and probably fine and deport you. So carry a tent and stay outside of the big towns.  You'll also need a stove and a water filter to survive. 

The routes

1. Yunnan to Lhasa route.
Take the Zhongdian to Deqin road remember to change money in Zhongdian its the last place before Lhasa. Deqin is a great town with a fab disco and a good place to get information on the state of the road its often closed due to landslides.
Deqin-Foshan 60km downhill moderate surface. Do not stay in Foshan there is a road workers station 3 km before and they will let you stay for 20Yuan. Fo shan police will turn you back so speed through here.
Foshan-Yanjing 50km very bad road flat. Pass the border post go another 10km before Yanjing where the first checkpoint is.  We crossed at night ( 3am )and the guards were sleeping. The checkpoint is floodlit and located 200meters before yanjing town. If stopped they will contact Markham and you'll be fined and turned back.
Yanjing-Markaham 120km bad surface.
Awesome scenery, the first shops outside Yanjing are 20km along the road near the mountain pass. Over the pass are great camping areas and there are many villages for supplies on the route to Markham.
Markham! Dangerous place to stop although we heard of people who refused to leave being ferried towards Lhasa by the police as long as they left the county. 
Markam-Juka 60km moderate road surface. Out of Markham a climb of 15km then a decent of 50km as far as the army base at Juka. Cross the river climb 3km to a truck stop motel.
Juka -Zuogong 100km moderate road surface. 
Climb 20km steep to 4000meter pass descend 20km to a little village for lunch, climb 30km to 5000meter pass, descend 30km to Zuogong. 
Zuogong is a county capital but there is no obvious police presence although it's full of soldiers and there is a nice guesthouse /restaurant at the far side of this one street town.
ZuoGong-Basuo 150km bad road surface.
60km to Bamba truck stop on fair road pretty flat slight uphill. 10km steep uphill to pass after Bamba then down on very bad surface 15km steep. Then gentle down along river to Basuo 60km, on bad surface though they were making the road as we passed by. 
Basuo police will stop you to check passports and let you continue, possible to stay here.
Basuo-Bomi 200km fair surface. 
Climb 30km to pass descend 30km to Rengou lake. Really nice section like the Alps. Sandy road for 100+km into Bomi. Last few km on tarmac.
Don't stay in Bomi, police will try to fine you ok for a provision stop though. 
Bomi-BaYi 200km. bad road
From Bomi the road goes down for 100km following the river into a rain forest with mud road, then climbs for 50km to a pass the town 20km short of pass has police be careful. Descends 30km to Lin Zhi on tarmac then 20km to BaYi.
DON'T STOP in Ba Yi police are looking for travelers to fine.
Road splits south route crosses Ba yi bridge and then 53km on sandy road to police checkpoint on bridge to Milin. Will turn you back so go  at night. German coming other way had no problems on this route.
North route 130km on tarmac to Gongpujiangda. Will pass many army bases for food. 
Bad road 60km to Jinda for guesthouse. 60km up to Songduo which has a guesthouse. 
From Song Duo steep uphill for 25km to pass then 25km on tarmac downhill to a small town with a great Tibetan teahouse for bed and food . It also has a hot spring. 
Hot spring village to Lhasa. 130km tarmac flat.
Finally on plateau pass many villages for rest and food.  
2. Southern Route.
Follow south route from Chengdu. Nearing border avoid towns and only camp. Before Markham you will pass a series of petrol storage tanks. Take the path to the right which goes around the police checkpoint and links up to the Southern highway the other side.
From here it is the same as the Yunnan route above.
3. Northern route. I don't know about this one although on the map there appear to be many options and the route is the main truck route so you can expect the road quality to be the best. 
4. Kashgar to Lhasa the western route. I have met people who have done this route and they describe it as hard physicaly but with no real police problems .

Legally

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.