All cash buyers go to the head of the bank's line, even ahead of a lower offer from someone who has contingencies for loan, appraisal, or whatever. If you're not an all cash buyer, make your offer as contingency-free as possible and be sure to have a pre-approval letter from lender. The bank wants it sold with as little risk, expense or difficulty to them as possible.
Finally, make your offer quickly - the first or second day on the market. If it's a strong offer, the bank may just decide to sell it to you and be done with it. Waiting is never to your advantage.
If it has been on the market for a while and there are no offers, then it is overpriced. Offer what you think it is truly worth based on actual comps, and if they don't take it, move on to the next property. You can always keep an eye on it if the price drops.