I'll go out on a limb: you *should* get the amp re-biased every time you switch power tubes. But... if you're replacing with the same model (e.g., EL34 -> EL34), you might get away without doing it. I have a JCM800 head that I got in the mid 80's - I've replaced the power tubes maybe 3 times and I've, um, never re-biased. I think the first swap may have even been from 6CA7 (which may have come stock? I had some loose ones and have no idea where I would have got them otherwise) to EL84. I was a teenager and not keeping track, and indeed had no idea what bias was.
The truth is that there will be a range of acceptable bias values, and unacceptable values on either side of that range that will result in crappy sound and probably greatly shortened tube life or other problems. The "good" range of bias values will be a little different when you switch tubes if the new tubes are a little different, and so if, with the previous tubes, your bias setting fell in the lower part of the good range, maybe it'll fall in the higher part of the good range with the replacements - sort of a crap shoot.
Also, it's worth noting that, inside the good bias range, changing the bias *does* change the sound of the amp a little, particularly with regard to break-up - so the amp tech who's setting your bias is using some judgment in coming up with the setting, unless you're sitting there with him/her and testing to come up with your optimal setting. That is to say, there's a chance that the interaction of the current bias setting on the amp with the new tubes will produce a sound that you like more. (and a chance you'll like it less, of course, and a chance you won't notice any difference with regard bias-affected sound attributes)
The point of this is that you probably don't need to worry about replacing say, the Ruby's with the JJ's, even though the descriptions on the website say they'll behave a little different. If, with the new tubes, the sound is really cold and lifeless (bad on the low side), or really farty and straining (bad on the high side), then maybe you have a bias problem and should go seek help (or put back in the old tubes). That hasn't happened to me with the Marshall, and I love the way it sounds.
now the disclaimer: I'm not an amp tech / electrician / EE, so take my opinion for what it's worth, and I also agree that the speakers and guitar/pickup/pickup height, etc. should be the first place you look to improve sound in the way you're describing.