How would one go about guessing the bid amount given the .eth name?
If you know which bid transaction is related to the name in question (maybe the account only sent one bid, and you know its name), then you can see the amount of ether sent with it. If you know the name, you can also see who started the auction. Many people start the auction and bid at the same time, so you can see the amount of ether sent on that. If the bidder did not disguise the bid, then you can see their exact bid.
How does adding extra "protection money" make that process harder?
If the bidder sends extra money, then you can't use the
value sent in the transaction to see the real bid. All you (technically) know is that the
value is greater than or equal to their real bid.
Is the difficulty correlated to the amount of extra ETH added?
Yes, if you are bidding the minimum. If you bid the minimum of 0.01, then masking it with 1 wei will not be very effective. There will only be two possible bid values.
Or is using a random amount better?
You are likely to make it more difficult if you make the bid truly random, down to the wei. If your bid is rounded to the nearest milliether, for example, that dramatically reduces the search space.
If I may add another: How much does masking your bid matter?
It doesn't seem to be important. Most bids are unchallenged at this point. I haven't seen any evidence of current squatters who try to guess at real bid amounts.
It will be relevant again when names under 7 characters are released, in about 2019.