The best way is to transfer the money directly from your bank account to her bank account. That way, both of you guys will have a record so if in the future there's an argument, you can have proof that u've paid her.
I think you better bring her to open an account. Try HSBC or Hangseng Bank. There shouldn't be a charge if she only use the ATM machine. It only charges money if you go to the counter to take money, if you go to the counter to deposit money there isn't a charge. Always find the big banks for more secure services.