Just to add my tenpence, I didn't find feeding to be all glowing and lovey dovey eye contact either!
I had huge trouble bfing for the first 4 months, DS was early, had tongue ties, and had a lot of formula in the first month due to his size. The incredibly un-fun combination of all these things made bf painful for months, so it was most def not a bonding experience! I used anything I could as a distraction, I never looked him in the eye while feeding, and watched a lot of shit TV. Things got better after 4mo, and were fine but not enjoyable for the next few months, but after 8/9mo the tide changed and it's finally a lovely experience! He's 12mo now, and feeds are lovely. I am really bloody stubborn
I talk to him about our day at his evening feed and he's often giggling while latched on, it's very sweet.
Don't worry about public feeding - it gets so much easier! I didn't get used to it for months as latching on was a nightmare, but now it's a piece of piss! Until it got easy I used a nursing cover, and varying scarves and muslins draped strategically... 
The difficulty you could run into with expressed bottle feeding is what happens when he has a growth spurt and needs more? As you'd be pumping, he wouldn't be stimulating your supply directly, so you would prob end up supplementing with formula, which in turn could diminish your existing supply. 
Sorry for the waffling... Hope it gets better for you soon.