I would say the the word "bid" is used in a context where you state an amount of money to a seller or a business in exchange for a product or service and you are competing against others who are also "bidding." (An example would be at an auction.)
An "offer" would be the same as the above but you are not necessarily competing against others.
To me, a "proposal" would usually encompass much more and would be something (such as a plan to complete a project or perform a set of services for a specific amount of money) that a business would show a potential client with the hope that the client will approve.
I hope this helps.