Ahhhh, welcome to poly land. Place where juggling is mandatory
It doesn't sound like you are gay/lesbian so much as you are experiencing some NRE over your girlfriend. That's cool. Why not, you aren't getting your sex needs met at home. I think I would just try and keep those feelings of possible gayness at bay for now and wait it out.
For a time I thought I was done with my husband because I was so over the top in love with Mono. It passed in time and I think it was a really good idea, in hindsight, to shelf those feelings as much as I could until our NRE passed and I could look at everything without rose coloured glasses...
It sounds like the sex thing might be a bit of an issue to him if he is concerned about being number one etc. and he doesn't have much sex any more. It sounds like he might feel threatened by her. Even more so if he knows he will be away for work and you will be around her more.
I think if I were you I would absolutely douse him with loving words, things he likes (his favourite meal or for instance), little notes, arrange special dates and holidays... that kind of thing. Show him now more than ever that he means something to you and that although you are getting your needs met elsewhere and love someone else also, that you are not about to abandon what you have built together.
As to her I think I would make sure that she knows that you will be lonely when he is gone and that you intend to do your best to stay connected to him and that you might need some help to do so by her reminding you to and giving you a little nudge in that direction if you get to needy. At the same time, this is a great time to really get to know her and spend quality time with her... really see what your relationship with her could become.
His being away is also a good time to spend with yourself. Really take a good look at what you want for your future, start something new, do some soul searching.... a good connection with yourself (you are you own primary) will make all your other relationships much easier to manage. At least in my experience.
This is all possible, it just takes time and pacing. There is no rush to have it all settled. The journey is what it is all about. Not the destination. Give it a chance and allow them to adjust. Allow your self to adjust. Just see what unfolds as it will and as it should.