It's just an amp. It's not some mythical beast to be feared or worshiped. OTOH, if it was a vintage SVT...
With any used amp, but especially a used tube bass amp, it is important to budget for a thorough inspection by a qualified technician. Unless a problem is discovered, a cursory inspection and tuneup (bias check) can often prevent worse, expensive problems down the road and most techs are more than happy to make many minor adjustments and suggestions which will help educate you about the amp and save you major expense down the road.
Read the Amps forum FAQ about tube amps, but be sure and read ALL of it, not just the first few posts. Some of the initial statements are addressed to tube amps in general and not tube bass amps, which can be much less forgiving of user error.
Tube life is a widely misunderstood subject. Put simply, unless you're touring and playing five nights a week, you should never have to replace any of the amp's tubes from wear in your playing lifetime if they're in good condition. I have 60's Fender amps with their entire original tube complement that still sound awesome.
As far as diagnosing any problems by playing through it, make sure there are no hums, buzzes or weird noises. If the amp powers up and doesn't fault and plays and sounds stable for an hour or so, chances are that it probably IS stable. Like any other amp, if it sounds weird or bad or funny to you, don't just assume that it is a small problem that can be easily fixed regardless of what the owner may say. Quite often, they are clueless or dishonest, and you shouldn't have to pay to fix someone else's problem.
If anything doesn't sound, feel or even smell 'right,' walk away. There are plenty of great reliable used amps out there and an amp you've never played in person doesn't always match up to the sound in your head. Don't be afraid to not like it, and don't think that you HAVE to buy it just because you think you should. Good luck.