How do you identify whether your RMSE score is good or not?
Note that RMSE is an easy to understand metric. Its the Root of the Mean Squared Error. So this is just how is the typical error.
If your target is something like how big is a building, and the mean of the target its 100m, then having an error of 0.3m its nothing. On the other hand if you predict the size of insect, and your target mean is around 0.1m then an error of 0.3m is huge.
For your case it seems like a good result, an RMSE in test of 0.3, in a range of [-3,3], but then this depends on your problem.