Both the BBA and Bottlehead are specified at between 85 to 95db signal to noise ratio. While these are fairly respectable numbers for tube equipment, no weighting, the way the specs are measured, is given. I suspect those numbers are 'best case scenarios' that do not reflect the way your Odyssey and SB are measured. Unless you're spending many times more $, for tube equipment, than what the BBA and Bottehead cost, your not going to get high s/n ratios AT THE FREQUENCY EXTREMES. The other thing to note is with the gain of the Odyssey you're probably not having to turn up the pre too much and, sometimes, the best s/n ratio is not realized untill you turn up the pre to a point where its working in its optimum operating range. So the tip about the attenuators is a good one, but it may not solve the problem if the inherent s/n ratio of the Bottlehead is just too low.
In the pro audio world this 'matching' of components is called gain staging. Its all about matching components so that they feed each other to work in their optimum operating range ie. where their s/n ratio is greatest and distortion is lowest.
If your source is a SB3, I seriously doubt if its the source of the noise, unless its broken.