The support for bech32 is indeed very weak but Bitcoin Core can also send to (and receive) this address if you compile from github source. The bech32 support was included in commit aa624b6. There might be some other wallets that support it because these transactions can be spotted in the wild from time to time.
I just thought I would update this to save anyone the effort of trying this themselves.
I just downloaded and installed Bitcoin Core: 0.15.1 Windows installer version released 2 days ago. For some reason, they don't seem to have included the ability to send to a bech32 address.