If you want to get Redbubble traffic, one of the more effective ways to do it is through social media auto-publishing.
Basically, you would publish quotes related to the saying on your T-shirt, or it has something to do with the design of your shirts, and you basically keep republishing this content on your social media accounts.
The easiest platform to do this kind of thing on is Twitter.
The downside is the traffic is kind of on the low end.
You can compensate for this by running many different accounts and targeting many different related hashtags.
It will also help if your posts are visually appealing.
Still, if you have the scale to do it and you set up your auto-publish system correctly, you should be able to send quite a bit of traffic to your Redbubble pages.