What You Can Bid
You can bid NIL or any number from 1 to 13, and the bid is yours alone: there is no partner to add it to, and no partner to blame. You bid after the draw, on the hand you finished building, so no card is on its way to rescue you. Count the likely winners among the 13 cards you hold, and bid that.
Estimate a Contract You Can Make
High spades and side-suit aces are the backbone of a bid, though a side-suit ace can still be trumped once your opponent runs out of that suit. The duel also changes what a picture card is worth. With half the deck lying dead in the discards, kings and queens win more often than at a four-handed table: a king with one small card beside it is close to a trick, and so is a guarded queen. Close is not certain, though, so do not count every card that looks high. A hand is 13 tricks, not 26, and every trick you claim is one your opponent cannot.
A Worked Scoring Example
Bid six and take eight: you earn 60 contract points plus two overtrick points, and add two bags. Bid six and take five: you lose 60 points, the price of a single trick too few. Ten accumulated bags cost 100 points, so habitually bidding low is no safe hiding place either. After each hand, hold your bid up against what actually happened and ask which of the cards you counted as winners let you down.