We have no idea why you cannot contact Bangkok Bikes Rental, try it in the early evening or early morning (Thai time).
For Big Bike Rental Bangkok, we have no experience with them, I have the idea that they are the latest bike rental company to open in Bangkok. If I look at the rental bikes they have on offer I can only see naked bikes (motorcycles without fairing), naked-bikes are nice to cruise Bangkok city roads, but out on the open-road touring Thailand I would advice to rent something that has some wind protection.
Especially if you not used to riding a naked-bike all that wind on your helmet while touring the country all day can give you some serious muscle pain in your neck and shoulders....
Bangkok Bikre Rental is not replying to my requests. No one picking up the numbers online. Does anyone has experience with www.bigbikerentalbangkok.com ?