2 mth old has been exclusively breast fed so far. No bottle feeding at all. Must we introduce a bottle, or is it ok to continue without a bottle?

You decide. Breast alone can certainly fit for most mom/babe couplets for this process. If you chose to offer a bottle,ever,let it be someone else when you are not around or baby will not cooperate.Having a backup feeding plan for unexpected events, like maternal surgery, unexpected separation is worthwhile for some.Total BF kids can really struggle if is is forced on them by necessity.
Breastfeeding. Breastfeeding is a time honored and healthy way to bring up a baby. Women have breastfed a baby to 3 years and more. A bottle is not necessary if breastfeeding works for you. Baby can go to a cup when s/he is ready.