The old warhorse in this connection is Bray Hammond’s Banks and Politics in America from the Revolution to the Civil War. Hammond concludes generally that the second BUS gave the United States the most stable money supply it has ever had. Here his thinking reflects Milton Friedman’s idea that what is ideal is for the money supply to grow at a low, steady, predictable rate over time. By his reading, the Panic of 1837 resulted from Jackson’s economic policies, including the Bank Bill Veto, Removal of the Deposits, putting federal funds in the Pet Banks, and the Specie Circular. A good short introduction to that is Robert Remini, Andrew Jackson and the Bank War, which although heavily slanted in favor of Jackson (who was Remini’s idol) gives a clear account of the major issues. For my money, the best account of the financial issues in high politics during the Jacksonian era is Irving H. Bartlett, John C. Calhoun: A Biography. Calhoun fathered the Independent Treasury created by Congress during the Van Buren Administration, which performed excellently and satisfied the constitutional requirements.
No, the BUS did not print currency, but it did issue bank notes–which served a similar function. (Jackson thought this delegation of power was unconstitutional.) I’ve never heard anything about his disliking the Bank because it didn’t (couldn’t) print money.