Reddit mentions of Calvin Klein Women's Lux Stretch Pencil Skirt,Black,10

I think chinos might be too casual for a bank job where the dress code calls out suits and suiting separates as acceptable daily wear. In my head, dress pants means something more like these wool trousers than than these cotton chinos.

I suggest you buy some suiting separates and wear those for your first few days of work. You'll be able to observe what the other women are wearing and then decide if your chino pants are sufficiently dressy.

Here are some example pants and skirts that should be appropriate:

• Calvin Klein pencil skirt
  
  
• Banana Republic straight leg pant
  
  
• Ann Taylor pencil skirt with flounce