I went to Burma for two weeks last November. There are foreign offices in Bangkok, Hong Kong, and Kuala Lumpur. As far as I know only the Bangkok office has express, same day visa turnaround service. Unfortunately when I went much of Bangkok was under water and nobody was picking up the phones at the embassy, this is probably just normal though. I rerouted through Hong Kong to get my visa, not knowing if they had same day service. As it turns out, they don't. Luckily they did get it processed within a few hours. They may or may not ask you for a business card, they don't want press people for some reason
I continued on to Bangkok and flew Air Asia into Yangon. The comments about bringing cash are absolutely critical, and bring uncirculated US dollars or you'll be getting shitty rates, if they'll exchange them at all. I had all uncirculated US currency, a couple of hours before exchanging the money I put a few $100 dollar bills in my wallet. The miniscule crease that resulted caused the money changer to reject them. On the other side any Myanmar currency that's taped together or in tatters is perfectly acceptable. I recommend putting your currency in a tin box (ridiculous I know).
Burma was really worth the effort. Kind people, very interesting places to see, and a fraction of the visitors you come across any where else in asia. This will change.
I have quite a few images from Burma on by blog. Republic Of Mike