Any 19-yr-old car, regardless of the mileage, might have a problem with gear slippage. The bands could be a cause of the problem as well as the transmission control module. No one here can tell which it is, but both are not one of the more inexpensive repairs.
I'd have the problem looked at by trusted licensed mechanic. This sort of problem won't go away on its own . It will get progressively worse over time, wasting gas and could eventually cause a safety issue, not shifting when you have the need to pass quickly.