"Do I have to pay sales tax on my new bicycle?"

Short answer: Maybe

Shipping it to you
We don't have to charge anyone sales tax if we are shipping the product to a destination outside of Washington state. So if you don't live in Washington, or even the United States, we don't have to charge you sales tax if we ship it to you. This is true for all companies in the United States.

If you pick your bike up in Seattle, then we have to charge sales tax, but you may be able to request a refund depending on where you live. If you live in one of the states, territories, or provinces below, you qualify for a refund from the state of WA.

Here's the pdf form with more details.

Here's the link to the Washington state gov. page showing how to apply for your refund.