Is there an alternative to Bloom filters? There have been a few papers, online publications and discussion about the negative effects of bloom filters on privacy.

What are the alternative to using bloom filters?
(bonus question: Are there any improvements we can make to bloom filters?)
I assume you are talking about BIP 37 which uses bloom filters for SPV wallets.

Currently there are no alternatives to BIP 37 for SPV wallets. However roasbeef is working on a proposal for client side filtering, which you can read about here: https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2017-June/014474.html. Client side filtering is an alternative to using BIP 37 and should work much better than BIP 37 does.