Ahh, I see. I was confused about whether semi-supervised approaches rely on using predictions on the unlabeled data to improve model performance. Wikipedia seems to suggest this is a key component which isn't mentioned in OP:

> Semi-supervised learning may refer to either transductive learning or inductive learning. The goal of transductive learning is to infer the correct labels for the given unlabeled data.

Agreed on bootstrap, but in the proposed approach you're not artificially expanding your sample size by sampling with replacement.