Oyster cards are rapidly becoming redundant, as most people simply use contactless debit cards instead. So your friend could do that (and you could use the money you've saved to buy her a little gift).
The single fare between Kings Cross and Hatton Cross (or vice versa) is £5.90 at any time if paying by cash. When using either an Oyster card or a contactless debit card, it's £4.70 on Monday to Friday from 0630 to 0930 and between 1600 and 1900. At all other times it's £3.10.