All of us have credit cards but they are the US style with a magnetic strip – not the European kind with a chip. Where possible, we will use the card(s). We do understand that many small vendors will not accept a card. There will also be small incidental expenses. Thus, can you suggest an amount of cash we should bring and change in to Bhutanese currency when we arrive? Perhaps suggest a range from ____ to ____ (low to high) from your experience with previous clients

For larger purchases like expensive carpets, or Bhutanese traditional dress, some legal artefacts, thangkhas etc. you can use credit cards. For trip of 14 to 15 nights, I would say bring at least 400$ in cash. You may or may not use it but it is good to have. Debit/Credit cards works here but only bigger establishment accept them but not the smaller vendors.
As for ATM or Debit cards, ATM machine are not reliable in terms of its workability. So bring some cash for your daily expenses such as for beer & hard drinks. For easier transaction, you may change into local currency in airport or bank.
Ensure to have exchange receipt, if you have surplus at the end you may change it back.