Upperbound on the degree of a boolean function in terms of its sensitivity
This paper came up on the arXiv today and it improves on the upper bound on $bs(f)$ in terms of $s(f)$. They prove the following bound:

$$
bs(f) \leq 2^{s(f)-1}s(f).
$$

This along with the connection that Marcos mentioned in his comment should give better bounds than previously known.