Good starting point, you're better now than most are when they get into it..
The first thing that I noticed is that you don't tighten your back - you need to squeeze your upper back, your shoulder blades and your lower back together. I saw a Dave Tate video on You Tube where he pointed at a spot between the shoulder blades, and said that you need to be pulling everything towards that spot. It gives you a solid foundation to start with, and you do it before you walk out. Set up, Squeeze, lift and walk out.
The second thing that I could see is that your first movement needs to be with the hips. Right now, you're bending your knees, you need to push your ass out back behind you - think about how you sit on a toilet, it's like that.
Pretty good, but if you want to lift in the IPF/USAPL, you're feet need to be flat on the floor. I think you could also set up a little further towards the bar, the distance between the rack and your starting point looked a bit too far. All told, though, you've got really good bench form.
I used to do the same thing that you do, my hips would move up, my legs would straighten out, my back would round, and THEN the bar would start to move. I came up with a pretty home-brew fix for it... When I walk up to the bar, I posture myself as if I were going to jump as high as I could from a standing start. I set my feet a little wider apart than I used to, my heels about shoulder width and my toes pointed out a bit. I make a point of flexing in an exaggerated lockout position, really arching my back and pushing my hips forward. It looks a little silly, but I find it helps me to focus on the right muscle groups. When I bend down to get the bar, I arch my back, take a deep belly breath, and rock side to side to set up. When I lift, clench my hands, my shoulder blades and my glutes first. I push down into the floor with my heels and pull backwards with my upper body. I thrust my shoulders and head back, and imagine the bar path tipping me backwards, not straight up.
Hope this helps, I know that it's long winded, but it worked for me.