Before tweaking the bias voltage (you need to own a wide bandwidth AC Voltmeter for this), I'd recommend just doing a test. The bias should be very close to ideal.
Try recording a sine sweep from 30Hz to 16kHz (the free mac/pc program Audacity will let you create this sweep tone) at -10dB on your meters with DBX switched off (the EQ set to the middle natch). The manual specifies +/-3dB for this range. Make sure the tape path is clean. Record the sweep and then play back and note the frequency response.
If you want to be sure it's working well, I'd also recommend verifying the azimuth of your machine (which is far more important IMO than a tiny bias tweak). A rough way of doing this would be to record a 10kHz tone on channels 1 & 8 at -10dB. Play back the tones with the input monitor down but the channels 1 and 8 inputs' set to 'RMX'. Pan the tracks hard left and right and use the fader to bring them both to about -6dB on the master VU. Next, pan the channels to the centre and check that they 'add'. Ideally, you'd see a 0VU but on such a narrow track machine any noticeable reinforcement is probably OK (the service manual suggests shooting for <90º phase error, which is a little too lax a standard for my taste). You can read more about this approach on
AnalogRules.
I've had no problems with country-laning on my 388 switching between tape brands. Like Cory said, it's wear related. If it affects your machine, it's not hard to diagnose. The tape will noticeably ride up and down the head and sound weird.
You could also just try the machine with the new tape. And if it sounds good, it is good! I love the 388 but it isn't a Studer A820.