Unfortunately, an ADN with a BA or non-nursing BS is not considered the same as having a BSN, since you probably didn't cover nursing theory, community nursing, research, etc. in your BA/BS program
A lot of hospitals out here are Magnet or trying for it, and so they strongly prefer BSNs. ADNs do get hired, but often they are internal employees of a facility, already enrolled in the RN-BSN program, or networked like crazy during their clinical rotations. I'm a ADN/BA who was able to get hired at a major hospital in CA...but I'm also an ADN/BA in a RN-BSN program, and also with experience and specialty certification, so that helped a lot (whew!)
Since you're going to have a BS shortly...have you considered an accelerated or second-degree BSN program? Time-wise they're about the same as an ADN program, maybe a little longer.