How long does it take to travel from the Westeros East coast to Asshai? How much further is it from the West coast?

Well, from Sunspear to Qarth is 4,690 miles, and then Qarth to Asshai is around 2700 miles more, so that’s ~ 7,400 miles. Assuming an average speed of 160 miles a day, that’s 46 days…if everything goes well.

Going from Oldtown instead adds 1,760 miles to your journey, so add on another 11 days.