There are not any rescue shelters in the United States as of 2015 that deal exclusively with Bichon Poodle mixes. However, there are rescues that are dedicated to small dogs only, such as the Small Dog Rescue Humane Society in Georgia.
There are also rescue groups and dog shelters that are devoted to the Bichon breed exclusively, such as the Delaware Valley Bichon Rescue in Cinnaminson, New Jersey. The Poodle breed has its own exclusive rescue groups and dog shelters as well such as the NorCal Poodle Rescue in Walnut Creek, California. A person who is interested in adopting a Bichon Poodle mix may need to contact a variety of general rescue groups before finding one.