Breast milk is actually pretty sturdy stuff rebelmum so you can happily add to small amounts in the fridge and leave it there for a few days, or freeze larger amounts.
You can also keep your breastpump in a clean (obv!) plastic bag, or wrap the cup bit in clingfilm and store it in the fridge if you use it more than once in a day - just wash and sterilise at the end or beginning of the day, whichever is convenient. I actually just clean it well in very hot soapy water and leave it to air dry.
It might also be worth giving breast shells a go if you tend to leak from the opposite breast when feeding. They can collect small amounts of milk during a feed and it all adds up.
As far as when to pump, it really doesn't matter imo, it's not going to make a lot of difference to what your dd gets if you're just expressing an oz or so at a time. The amount you can get while pumping doesn't equal what's actually there - your dd will be way better at getting milk than a pump! How about trying to pump a little bit before and after each feed? Again it'll all mount up.
If you want to get more at once, I find that getting up in the middle of the night works best (unfortunately!), but it might be worth it if it's a one off.
Again, if it's an occasional bottle it won't disrupt your supply at this stage but you may find that you're uncomfortably full because you missed a feed. If you can get some time with a breastpump at this point then you'll probably be able to replenish your stock! Make sure you know how to hand express so you can express off a bit into the sink or something to make yourself more comfortable.