IB flies from MAD to both ZAG and DBV but they are both seasonal destinations. You can try BA into DBV but that service operates from LGW. If you want to get creative there are also IB flights from DBV to VLC and BIO during the summer. The only other partner flight into ZAG is MA from BUD, as you already mentioned.

My suggestion, since this is an AAward, is to try for LAX-JFK-BDA on AA, then BDA-LGW-DBV on BA. No messy London airport transfer, superior BA product across the Atlantic, and a free stopover in Bermuda if you want it