When you copy a bid from one database to another, existing records (Items, Item Types, Condition Types, etc.) in the destination database will be used, if they exist. Records that don't exist in the destination database are added. Payroll Settings are "encapsulated" in that bid, however, and are not affected by settings in the destination database.
When you copy/paste or move a Bid that includes eQuotes from one database to another, those eQuotes, including the Suppliers and any returned pricing, are retained. However, if you export a Bid, only the Materials of an eQuote are included, not the Suppliers or any returned pricing.