Went out today for the first time since lockdown..q

Little is now 6 months so takes everything in she feeds on demand however out today she wouldnt take the breast for a feed i know its so hot so my question is....

Can i hand express directly into a sippy cup and give it to her as she drinks water from one (its free flow)

Or

Of i take a sterilised bottle out with me can I hand express directly into that

Now are both of these ok or bacteria risks i didnt think would be any different to expressing into a bag

Also say I did one of these how long would the milk be ok for

But also if it was really hot I could use a cool bag