Frankly, after the last two singles (which I don't think represented the strength and depth of the album very well), I'd be glad to see almost any other track released!
That said, I'm not as sold on "Drinking Alone" as many of you are. Although it has an interesting theme, which strikes a realistic emotional note, and adds some further variety to the image that Carrie projects in her songs - I'm not too keen on the choppy, semi-spoken vocal line in much of the song, which I don't feel exhibits Carrie's talents as a performer as well as some of the other tracks. Also, the mixture of Country tradition with progressive influences from General Music - which is characteristic of much of the album - could, in my opinion, be better shown by several of the other songs. This is probably a rather unpopular opinion - and I could certainly live with DA - but I do rather hope she looks elsewhere.
(Leaving aside "Cry Pretty", only because it's already been used) the four strongest remaining songs, in my opinion, are "Low", "Ghosts on the Stereo", "The Bullet" and "Spinning Bottles" - and whether we get one or two more singles, I'd like it, or them, to be from that group. (I do like "Kingdom" as well - particularly for its commitment, and strong build up of musical and vocal force as the song develops - but it is effectively the album closer (treating the Champion as really a bonus), and Carrie usually treats the closer as a special song, where she expresses a meaning close to her heart, but doesn't use as a single).
"Low", and "Ghosts on the Stereo" are both personal to Carrie, where I think she reveals inner feelings that go deeper in emotional realism than almost any of her earlier songs. Either would, in my opinion, do her considerable credit in stature as an artist. Of the two, "Low" is probably likely to be the more generally popular, and the one that gives her the greater vocal range. But both these songs come from a painful period in Carrie's recent life, and as we've already had "Cry Pretty", which expressed the turmoil of being in the public eye as an artist, regardless of feelings as a person, she may not want to choose another song with a theme that expresses such personal sadness.
That leaves the two more general "issue" songs, which again, I think, would raise many people's appreciation of Carrie as a mature and varied artist of depth. I actually think "Spinning Bottles" is the stronger, and more unusually themed song - and perhaps the best on the whole album - but it doesn't strike me as a song that lends itself to frequent repeat performance, and may be quite difficult to sing (perhaps, rather like "Forever Changed" in an earlier era).
So we come to "The Bullet". While I don't think the Dan Beeson tweet can be taken as necessarily definitive, I do think this is quite a sound bet - both for it's quality as a song, and the topicality of the theme, which allows Carrie to express a lot of emotional strength, without it being focused on her own life. When I first commented on the album, I mentioned the possibility that this song could have a similar implication for Carrie's career as co-writer Allen Shamblin achieved earlier for Miranda with "The House That Built Me". Yes, his songs can contain a political dimension (and while in THTBM, it was more oblique, and probably missed by many listeners, in TB it is more inescapable, for those who want to focus on it). But I don't see that as a crucially off-putting concern. The main focus of the song is on the lasting after effects of violence, and it doesn't take an explicit stance in apportioning blame, or in calling for any particular political response. Carrie is good at empathizing with people's loss, and her delivery is likely to stress the emotional effects, rather than the general climate of debate. Also, we should not forget that LW also began with a verse outlining the effects of a shooting (and Carrie herself co-wrote that verse). I do feel that that theme, beginning the song, may have affected the call out reaction to LW - but Carrie clearly put the importance of the theme first, and may well want to do so again. In my view, the rest of LW suffered from being too repetitive and generic to fully recover from an apparent partially negative reception from some listeners - but TB is much stronger in the lyrics dealing with the ongoing effects on families, and I think it will give her more scope to give a really impressive interpretation. It has to be said that any reference to this topic is potentially going to cause knee jerk reactions from some - but if we let that ruin a song's chances we would be losing a lot of positive value - and I think Carrie is too committed to her art to let that stop her. The album deserves a strong song, and while we have as yet no firm proof that this will be the one, it would neither surprise, nor displease me.