Which database are you working with? Do you know that there are not solutions already out there?
It depends on whether your database developer has access to Raiser's Edge and the API module or not. It also depends on how automated you want the process to be.
It is possible for you to get away with paying nothing for the API if your developer creates a plugin for you. In order to run a plugin you do not need the API module. Having said that unless your database developer has experience with the API it is unlikely he owns a copy of it. What is more it is unusual (but not out of the question) that a developer who specializes in their own database is also sufficiently skilled to create a robust application to transfer data between the two.
If the developer does not have access to the API then you will have to either purchase that module or alternatively the VBA module.
If you want a totally automated transfer of data then the API is the only alternative as with this you can create stand alone programs that can scheduled to run whenever you want.
If it is sufficient that the transfer is run on demand by running a macro within RE then VBA module will work very well. It is also much cheaper than the API module.
BB clearly are a very good choice to do this work but not the only choice. There are many independent developers that do this type of customization.
If you need any more information then please do not hesitate to contact me.
David