Early on in my world I wanted to create a whole lot of honey blocks, for honey furniture and that queen bee summoning thing. It was a bit of pain going through all the effort to fill 50 buckets with honey, and only getting like 1/2 blocks per bucket by throwing it in water. Then I discovered this way, which often gives me up to 12 blocks, and sometimes more, per bucket of honey and 4 buckets of water:
1.) empty two water buckets on top, and one honey bucket at bottom
2.) pull lever, mine the honey blocks (there will still be a layer of honey left) and pull lever again
3.) repeat once more

Is there a better way? I don't have access to pumps yet.

Try doing a search for "terraria water duplication" on youtube. That should give you a lot of different ways to play around with this.