i think you can try latching him when you are out.
not a good idea to bring out ebm: you can't leave it more than 4 hours in room temp and may waste it if he's not hungry at all, also quite troublesome as you have to bring hot water to warm the milk.
if you are at hospital you can use the nursing rooms. i dont't use any particular nursing cover, just my own shawl or baby's blankie then safety pin it in the centre and pull it to the side to cover (save cost, nursing items exp, hee). a good nursing top also helps a lot