Consider replacing "expensive" with another adjective like "great" which has a simpler comparative "greater".
*How many times more expensive is A than B?
Wrong, like "how many times greater is A than B".
How many times is A more expensive than B?
Grammatically OK, if you are looking for a ratio. Like "how many times is 10 greater than 2"? The answer is 5.
How much is A more expensive than B?
*How much more expensive is A than B?
Following the same logic, the second sentence is incorrect. The first is borderline - I would consider it OK in casual speech. See below for possible improvement...
...some other ways to express the same idea...
An good way would be
- By how much is A more expensive than B?
This asks for a difference, not for a ratio. An answer could be "by $1".
By how much is B cheaper than A?
How expensive is A compared to B?