Fans will always see a big "Follow" button on your Bandsintown artist profile if they're not tracking you yet, and it should already be an important part of your Smart Link. That button could also say whatever you want, like "Track On Bandsintown" below.
You can also have just that button displayed anywhere else on your website to encourage more followers. Fans who click that Follow button will start tracking you automatically without being sent away from your website.
Find the code and more information about creating your own Follow button here.
Don't forget to replace "your+artist" in the code with your actual artist name on Bandsintown!