Mothercare usually has a feeding room 
.
It's up to you. If you Want to 'get over it' then is there a friend or indeed a group from any ante natal or nct classes you did who you could meet who would also be feeding, safety in numbers etc. or could you go along to a bfing group in your area - the ultimate safe place to try? I found the usual thing for me of it never again being the first time was quite a thing - once I became someone who HAD fed in public, I could be someone who feeds in public iykwim?
Don't think I actually told you the story of my first effort though? I had chosen a small cafe in our local village on a random Tuesday afternoon so it would be quiet. They have a bf friendly sticker in their door and everything, and it was deserted. Perfect, so I got my hot chocolate and slice of brownie and got DS ready to go. And literally as I was sat there trying to get him to latch on (in the early days he could be a real faffer) this entire family of 14 turned up and filled every chair in the place including all the spare ones at my table. Because they were all together everyone was looking round much more than normal (no politely ignoring the table next to you) and 2 women in the group were alternating between trying to peer down my top at DS and tell me how cute he was and shouting at the room that this lady was trying to feed and they'd put me off if they weren't careful well, they were right. I got totally flustered, DS couldn't work out why he was suddenly being hustled along so much, so kept pulling off and eventually I just stopped trying, downed everything in one, and rushed out - only realising that I hadn't paid when I got outside and so having to sort that out with the waitress from the pavement cos I couldn't manage to get the buggy back in with all these people. It was such a failure, but as I found myself almost in tears on the way back to the car 'because they had spoiled what was supposed to be my first time' (ooh err) I realised I had to get back on the horse. A couple of days later I went to John Lewis to use the feeding room, but as I walked through the cafe saw there already 2 women feeding there. S I got a drink, sat down and did it then. And actually, the busy-ness of the place made me feel more anonymous. And it was ok, and then it was never the first time again.
I did however practice feeding with a scarf at home so both DS and I were used to it. Tbh I don't always bother with it now, but its useful for holding his feet! And that top I linked to helped too - it is very discreet and easy to use without a lot of faffing about. And I practiced with that at home too.
Final tip, I wake DS to feed when it suits me when we're out. I don't wait for hungry cues, he's usually more than willing to sleepily plonk on a boob (ha, autocorrect tried to have him Plonko-ing on a boob) without screaming the place down that way,
However, as Soyo says, if you actually decide just not to bother, then why not take a bottle of EBM with you, easy as you can store for 6 hours at room temp so no need to faff trying to put formula together in public. It's still your milk and you say you're expressing anyway? No need to tie yourself up in knots over it. Do what you're comfy with. By feeding him at home you are doing great. Don't knock yourself over something like this.