Levelshifting 3->5V. Can I add a DC bias of 0.5v or so to the 5v input line to bring up the 3v signals?

Assuming it doesn't just line up correctly, eg: If my Vih is 3.6v on the 5v side, and my Voh is 3.3v on the 3v side.

By DC bias I mean connecting up a voltage divider giving 0.5v to the line connecting the 3v->5v.

I'm guessing this isn't done as it would drain power when the 3v line goes low, but if the divider is high enough resistance, that could be minimal?

No, you will run into the noise margin of the two systems.

What are you trying to do this for ? Logic level shifting ? If you use a 74HCT gate, you will find the input ranges from 3..5V tie up nicely.
Other than that, the proper answer is a logic level shifter, like the 74LVC245