Posting this because when I tried looking around online there was seemingly no definitive answer for how to remove bubble solution out of white clothes, so here's what worked for me:

1. Sprayed the stains down with bleach spray. (I just used a kitchen surface cleaner with bleach, nothing specific for clothes.)
2. Let that work for 15 minutes.
3. Rinsed the t-shirt with water and wrung it out.
4. Rubbed a good amount of dish soap on to the stains, letting it froth up a little with the residual liquid in the fabric. (For this I used Fairy Maxi Poder - I live in Spain but I know the brand Fairy is available a bunch of places. But dish soap is dish soap.)
5. Left if for another 15 minutes.
6. Put the t-shirt to soak in a bucket of warm water and left it overnight.
7. In the morning, I wrung it out a little and threw it in the washing machine on a quick cycle (30 minutes, 30C) with some laundry detergent (Omino Bianco's Marsella, but I don't think the brand made a real difference.)   

And boom, the stains were gone.

This was after trying a few different methods, but I know this is the process that worked in the end because there were stains all down the front of the t-shirt and I was only working on the ones at the bottom. When they finally came out I repeated the same process on the stains at the top and they came out too. 

I thought the bleach didn't do anything at first as I expected to see a difference after 15 minutes, but I tried just doing steps 4 to 7 after I removed the bottom stains and it did nothing. The bleach is clearly important here, so maybe not a great option for people with bubble solution stains on coloured clothing.  

Finally got bubble solution out of my white t-shirt