Select the bell tab in your inventory, choose the amount of bells you want to take out, and a sack of bells will appear in one of your slots. You can add to the amount by doing the same process and combining the bags into one sum. You have the option to drop the bag of bells onto the ground, which the other person can take.
The only way to do that is by visiting their towns and paying them back that way. Same for shopping.
Make sure if it's a big purchase or many purchases that you have room in your pockets for however many money bags you might need. You might want to use your own ATM to withdrawal the bells needed as I'm not sure if you can use their machines. The money bags can hold 99,000 bells each as with the maximum you can carry normally. Hope this helped.