Archimerged has found some data for air bubble behavior. There is a graph of bubble size vs velocity on page 67 of this pdf file. Very slow bubble rise is possible for 100 micron bubbles. The problem is those bubbles also don’t rise after leaving the bubble pump and trompe. It becomes clear that either some mechanism to trigger bubble separation is needed, or a large separation chamber is needed at the top of the bubble pump and the bottom of the trompe. But at least, if the separation chamber is very shallow and wide, the forward flow velocity need not drop much while the distance the bubble needs to rise to reach the surface can be just a few cm. Bubbles rising at 10 cm/s would reach the surface in under a second, meaning the separation chamber needs to be under ten meters long. Inconvenient but not impossible.
The ratio of water speed to bubble rise speed would apparently be a lower bound on inefficiency: if the bubbles rise in still water at 1% of the speed of the water, e.g. 0.1 m/s vs. 10 m/s, then in the bubble pump the water rises at 10 m/s while the bubbles rise at 10.1 m/s and in the trompe, the water descends at 10 m/s while the bubbles descend at 9.9 m/s. Then the bubble pump and the trompe both lose 1% efficiency, leading to at most 98% efficiency, while break even would be around 95%.
So maybe we need slower than 1 in 100. Bubbles 0.2 mm in diameter rise at about 2 cm/s. With water moving 10 m/s, that is 2 in 1000, and the bubble speed accounts for an efficiency loss of 0.4%. The separation chamber must spread out so widely that that the water is only 2 cm thick and it must be 10 meters long. Actually, that might make it wider than it is long, depending on the volume. And it has to be well insulated, and the separation chamber must be at around atmospheric pressure: the bubbles have to separate before the water descends to the heat exchanger.
At the top of the bubble pump tower, that is kind of inconvenient, to say the least. Some more clever ideas are needed…
It begins to sound like the bubble pump is made of fairly small diameter pipe, say 10 cm, and multiple pipes are used to increase the power. Maybe we are back with the hyperbolic shaped tubing which tilts to nearly horizontal at the top. This allows the water to continue at constant speed say 10 m/s (need to check the hydrodynamic drag to pick actual pipe sizes and water speeds) while the vertical velocity component slows to zero. Note well, the bubbles are confined by the top wall of the tilted pipe so their rise is slowed. Also they start getting separated before reaching the top of the bubble pump.