This is why I use a Bass POD... I had a TNT150 when I was starting out, and the hiss direct was huge! My Warwick Pro IX head has masses of hiss when on the tube channel (well, they're tubes, fer chrissake) but the clean is silent.
This did lead to a hysterical happening at a Gig in Reading arts centre: I set up as usual - I prefer the tube channel for a little more edge in my Funk - and the sound engineer said "wow, there's masses of hiss, can you cut it down?" - I fiddled a bit and got "no, it's still there, we'll use a DI box instead of the Amp DI out" (the back of this amp is like a space shuttle dashboard). He plugged it in, it made no difference.
Until I flicked to solid state and said "how's that?" and he said "wow, how did you do that?"