How much power is enough for B&W Nautilus 804's?

Good comments by the others. Some additional thoughts:

1)If the impedance curve of the N804 is anything like curves I have seen for some of the other Nautilus models, such as the 801, the 4B-ST will most likely not be able to drive their woofer sections properly in bridged mono mode. Note that the power rating of the 4B-ST in bridged mono mode is only specified for an 8 ohm load, and not for a 4 ohm load. The reason for that is that in bridged mono mode the amp outputs "see" a load impedance equal to the speaker impedance divided by 2. Since the speaker's impedance in the mid-bass region (at least for the N801) is less than 4 ohms, it will be seen as less than 2 ohms, which the amp will probably not be able to handle, at least in an optimal manner.

2)I second the question about what preamp are you using to drive the amplifiers, and can you also describe how the preamp and amps are all connected together (e.g., with y-adapters)? Depending on the preamp design and the interconnection configuration, it's possible that bass is being reduced as a result of either impedance incompatibilities (due to the dual loading) or level mismatches (if perhaps you are using an RCA output for one amp and an XLR output for the other).

3)Assuming that you are biamping passively (without an electronic crossover between the preamp and the power amps), using the 4B-ST in bridged mono mode might result in a gain-matching issue between the low and high frequency amps.

4)Assuming that you are biamping passively, you would probably not be able to utilize a lot of the power capability of bridged mono 4B-ST's, because without an electronic crossover ahead of the amps all of the amps have to output a voltage range corresponding to the full frequency range of the signal. Therefore you would not be able to turn up the volume high enough to use much of the power capability of the higher powered amps without overdriving and clipping the lower powered amp.

Regards,
-- Al

Almarg,
excellent comments & observations esp. #1 as I was also thinking along the same lines. I've bashed B&W enough here (despite being a former B&W owner OR maybe because I was once a B&W owner) that I decided to stay away. ;-)
Then I noticed that you were thinking along the same lines & just had to pipe in..... :-)

One more thing - just because the Bryston amps are high wattage does not mean that they can source large amounts of current. I did not find any specs for the 4B-ST (tho' I did find a 1992 Stereophile review of the 4B). If the 4B-ST is anything like the former 4B then I read that the DC rails of the power amp are 85V! Meaning that the power transformer must be 60VAC. I have no idea what the VA rating of the power transformers are for the 4B-ST but that would have give some idea of the power delivery capacity. At any rate, the output transistors must be fantastically high voltage rated to run at 85V. IOW, at 85V the current handling capacity of some BJT power transistors is severely degraded i.e. they cannot handle much current while remaing inside their safe operating area (SOA). Thus, you have the high wattage of the 4B-ST but might not have the current delivery capability that B&W speakers so -l-o-v-e-. Hence a bass that is lacking heft.
Looking at the 4B-ST chassis leads me to believe that this thought process is on the correct track.
If the 4B-ST was a current delivery power-house the chassis would have looked like a Pass Labs 350 power amplifier Or a Plinius SA-250, for example.

I run my system including the 804"s" with an anthem statement p5. works great.

I haven't owned N804's, but I've owned several b&w's, inc. Matrix 802's. No matter HOW much power I fed the 802's, the bass was never tight or coherent enough.

I sold them & bought Totem Mani 2's, way better bass (& almost everything else). So you might want to check out other speakers, & not necessarily floor-standers IMO.

Exactly, if you want bass similar to open E string of double-bass Bowers will be your worst investment.