I've come back from Myanmar a month ago and been asked for informations so maybe more people would need them :
You need a visa to enter Myanmar, they give you 28 days, non extendable but you can pay 3$ for each day overstayed.
I did mine in Bangkok, very easy, a lot a people though, it cost me 810 baths (25$).
No visa on arrival yet :)
In the embassy there is a paper showing which border you can cross by land : Tachileik-Mae Sai, Myawaddy-Mae Sot, Kawlthong-Ranong and Htee Ki-Pu Nam Ron.
I entered by Mae Sot, no problems, no questions about the bike.
From Myawaddy I went up to Mandalay (through Hpa-an, Kyaikto, Taungoo, Meiktila) 925km, nice road, bumpy at some points, after the border there is a mountain to climb, very steep, almost no concrete, quite hard, but after that it's almost always flat until Mandalay. The road goes through a lot of villages and cities, it can be quite busy sometimes but it's ok, you can find food and water everywhere on the way.
After Mandalay I went to Bagan through country side roads, very nice, crossing a kind of desert, more remote, still flat. Then from Bagan to Inlay lake through Meiktila and Kalaw. Kalaw is at the top of a mountain, going up took me a long time, several hours and be careful it can be very cold up there (compared to the plains), maybe 5-10°C by night.
Then I had to take a bus to Yangon, and from there I cycled back to Mae Sot, same road.
You will never see a tourist on the road (or maybe a cyclist :) ), all the foreigners go to the same places : Mandalay, Bagan, Inle lake and Yangon, and some of them are becoming very spoiled, they are the worst places I've been in Myanmar, gold award for Inlay lake, it's an industry of money, I don't recommend it at all. I loved Kalaw and the mountains around, beautiful. Bagan, very touristy but still interesting and beautiful, and Yangon, big, dirty and polluted, I liked too, so many influences, great food. Mandalay, nothing really to see. But each to his own taste :)
I won't talk about the pleasure of cycling through the villages, and discovering the people of myanmar, I let you do that :)
Accomodation can be a problem in Myanmar as you are not allowed to camp, there aren't guesthouses everywhere and they are not always cheap. And people are not allowed to host you.
I did camp, I wouldn't recommend it as it's forbidden but it was quite easy, the most annoying was the dogs "protecting" their property.
The military is ruling the country, you can see them very often around big cities, with foreigners they are nice and smily, be ready to be checked for your passeport anytime, there are many checkpoints on the road, mostly around big cities and after the border. They often asked me where I was going, meaning where I was sleeping.
The police don't care about you, they saw me several time at dusk, leaving a city where I could have slept, they didn't stop me.
I heard about cyclists being followed by army or secrete police I don't know but it never happened to me, and in the case you're caught camping, they bring you to the nearest hotel.
Cities I know you can find accomodation on the way to mandalay : Hpa-an, Kayikto (expensive, go to the golden mountain, 10km north for cheaper places), Taungoo, Nay pyi daw (but nobody goes there), Meiktila (expensive).
There are many places and roads closed to foreigners, and I haven't found any way to find out wich one is or is not forbidden. The locals and the police I asked didn't know. I guess you have to ask the army.
This web site lists which parts you can or cannot go in Myanmar : http://www.coupsdecoeurenasie.com/pages/Les_zones_accessibles_aux_touristes_mars_2013-4833103.html
It's in french but you can translate, and it's from march 2013, it may have changed already.
Anything more, just ask.