Yes. You can change your bid at any point in time during the bidding process. You cannot change the bid amount once you have been hired. But that still does not mean that your price for the job is set in stone.
Use close communication with your clients like you normally would if any unforeseen pricing factors arise while doing the job. Fairmarket dialogues and bid amounts are not designed to be contractual agreements. All contract signing and invoicing should take place outside of the Faimarket platform. Check with your local legislature to learn more about legal binding agreements in your area.