One bit is sufficient if you are just trying to arbitrage markets. For a couple billion, an NYC to Tokyo neutrino shortcut wouldn't be a bad investment.
NYC to Tokyo would require an unprecedented beamline angled deep down into the earth as well as a much more powerful proton driver to produce enough neutrinos to compensate for the 1/r^2 loss of flux.
And, then there is the neutrino oscillation resonance due to the high matter density as the neutrinos pass near the Earth's core just to mix things up.
The price tag for DUNE is a couple billion USD for a relatively "short" baseline of 1300 km and 40kton far detector.
All that said, if some fat cat trader wants to fund it, I'll help build it.
If so, I think the speed advantage disappears.
If you wanted to transmit a lot of information with one pulse, you'd use time domain slicing and synchronized atomic clocks.
Regardless, you don't need particularly high signal fidelity in order to arbitrage the market, just better than 50/50. The ~25ms they can cut off of the transmission latency is an eternity in market time.