Can't add Starbucks Card to Apple Watch "ApplePay", only wallet?

I have my Starbucks card in my wallet on my iPhone. However it only shows up in my wallet on my Apple Watch, not my ApplePay. I find it to be several extra steps to navigate through my apps, open my wallet, etc. Not to mention the screen times out after a certain amount of time and defaults back to the clock while I'm standing in line getting ready to pay. I wish it was readily available wth the "double click" Apple Pay button.