Bubble Columns will only appear in source blocks and not where water is flowing into.

In the attached image, the left only has the water source block at the top, the right has two water source blocks, one at the top and one at the bottom.

Left 1x1 will not produce any bubbles. Right 1x1 will only produce bubbles in the bottom source block, and will not produce any bubbles in the flowing water above.

Occurs both in Multiplayer and Singleplayer.