Doesn't matter how well you think you know your dog. They are still animals and some times react in unpredictable ways. People that have had dogs as pets for years were surprised when the dog bit a child that it's been around it's whole life. Better safe than sorry and keep the snake away from the dog.
To the OP, the snake probably bit you out of fear. Snakes are just as unpredictable as any other animal, it may never bite you then one day, "surprise!".
Oh god no I would never have my snakes around a cat. they are to unpredictable they think every thing is a toy. My little sister has this one cat thats mooder the h*ll to all of the other animals but my dog. I have no problem with my dog being near cause I can tell what my dog is thinking I know there is a a bunch of people that will say b.s. and say a lot more on it but I can tell you every move that my dog is going to make before she makes it and she knows her commands VERY WILL! Plus when my snakes have been out and the dog comes near they are the ones to go closer to see what it is. They aren't flecking there tong like they think its something to eat like they do when I put a mouse in for them.
Not to be a downer but the man whose dog killed his child said this animal was good with kids and would never harm any one.
Animals are unpredictable through and through, As are people. You can never say your pet will not harm your snake and vice versa.
Plus a snake doesn't need to flick its tongue before striking or biting.
Snakes are very predictable in the sense that any decisions they make are based on instinct rather than thought. A dog can be trained to do basic commands like sit, stay ect ect relativly easily by various training methods but a snake will never be able to comprehend any sort of command as they havn't evolved that far. If you rub a mouse or any other prey item on your hand and put it in front of a snake you are definitly getting bit because its instinct says its time to eat. If you rubbed a steak on your hand and put it in front of your dog it will most likley get licked and not chewed because he knows you aren't dinner.
Snakes can learn some things by repetition, a lot of times when you feed dead food they will not constrict after a while because experience has told them they no longer need to. The more you handle a snake the less nervous it becomes because he learns you are not a danger to it. With large snakes hook training is used to prevent bites. In this we lightly tap the snake on the head every time we take it out for handling and at feeding time the hook is nowhere in sight, if done from a hatchling they learn that the hook means its not dinner time and this usually results in less bites.
I should have clarified, the hook training method is generally only used with big species that will send you to be stitched up with a decent bite. Burns, retics and afrocks usually hatch out 18" - 24" so they are not to small but when they get to the 10-12 foot mark the less agressive attitude makes all the difference in the world.