Maybe I'm UNDERthinking this, but in a 2-player game, I'm going to simply ask myself 1) how much is my deck generating per turn, and 2) how many lost turns is 8 VP going to be worth to me, then bid accordingly. I might even go a bit lower if I feel my opponent's deck is not generating much money.
Your intuition is correct: you should bid less than your true value if your opponent has a meaningfully lower value for the 8 VP than you do. Long explanation why follows:
Assume two players (P1 and P2) for simplicity, and suppose that their values for the 8 VP are common knowledge among the players. P2’s strategy is simple: bid one more than P1 if they prefer that to P1 winning with their current bid.
Suppose the 8 VP is worth <6> to P1, but <11> to P2 (for simplicity I’ve picked integer values but this probably isn’t the case). Consider P1’s decision. If P1 bids <6>, P2 can get it for <7>, which is “surplus” of <4> to P2. But if P1 bids <10> (so that P2 can’t get any surplus from bidding) P2 will recognize that and let P1 have it, for a surplus of -<4> to P1. So P1 wants to split the difference so that P2 doesn’t have any much better options (this is a “Nash equilibrium” in game theory). If P1 bids <8>, then P2 gets a surplus of <2> from bidding and P1 get a surplus of -<2> if P2 doesn’t bid. Both of these are a better outcome for P1 than if P1 naively bids their value of <6>. And P1 can’t reduce P2 below a surplus of <2> / boost themself above a surplus is -<2> at the same time, so <8> is the best bid.
Now suppose the opposite is true and the 8 VP is worth <11> to P1, but <6> to P2. P1 definitely doesn’t want to bid their value of <11> because then they get zero surplus. But P1 doesn’t want to bid only <6>, P2’s value, either, because then P2 will overbid and get it for <7> and only -<1> surplus. P1 bidding <8> means that P2 can overbid but has to take a -<3> surplus, or if P2 doesn’t bid P1 gets a <3> surplus. So <8> is also the correct bid here.
Now, what is 8 VP worth in debt? If it’s time to start greening, +8 VP is more than a Province and it’s an advantage that it doesn’t clog your deck (Tournament games excepted). Also, it’s easier to pay <8> than it is to hit $8 in one turn because you can spread it over multiple turns. So if both players are ready to green by buying Provinces, the winning bid should be more than <8>. If you have the same value as your opponent (let’s say <10.5>), then the strategy as P1 is to bid just less than that value. So P1 bids <10> in this case, and P2 can’t overcall without bidding more than their value.
Purely speculating, but the person gaining the first Province will have the upper-hand. If I gain it, then even if my opponent doesn't want/need the VP, they will still pretty much have to bid at least something for it, so that I don't get it for free. And then, I'll have the option of just letting them rack up the debt if I want. It reminds me of the you-cut-I'll-choose situation -- the cutter's (the one not gaining the first Province) best-case-scenario is they get an even share of the cake, while they chooser's (the one gaining the first Province) worst-case-scenario is they get an even share of the cake and their best-case is they get everything. Not a 100% comparison, I just thought of it.
You can see from the example above that the person who gains the first Province does not inherently have the upper hand. If values are equal, the first player to bid (the player after the one who bought the Province) does better. Intuitively, that happens because you need to overcall by <1> to win. The key to doing well is to have a higher valuation in debt for the 8 VP than your opponent, which may be related to being able to buy Province first - not the order of bidding.
Why would players have different valuations in debt for the VP? You may be ready to green and your opponent isn’t. For example, you’re playing a money strategy while they’re building an engine that hasn’t built a lot of economy yet and doesn’t have gainers so debt would be crippling. Or they’re playing a strategy that involves a lower money density (such as a Gardens or Silk Roads slog without gainers) and would lose many turns.
What about 3+ players? The bidding logic outlined above still applicable, but is more complicated. Also, players may prefer that one of their opponents win the bid as opposed to the other.