The bloom basically gives us 2 things, an easy way to detect typo's and in the event of a brute-force attack, it yields a significant number of false positives which all require a full scan of the blockchain, which I thought was a nice trade-off for the lower number of entropy bits.

If that first feature is somehow not effective enough, we could either tweak the bloom arguments or move to the 16 bit method that gmaxwell proposed.