Are you paying for two Internet services? When I was using Earthlink as my ISP, I could connect either via DSL or dialup to my Earthlink account. In such a case, you could use dialup for banking if you want, but I would not pay for a separate dialup service just for banking.
As BC_Programmer said, with proper security measures, you should not worry. That includes a firewall, of course, You should have at least SP2 if using Win XP, and keep your browser updated also. If you're using IE 6, i suggest you upgrade to IE7, or the latest version of Firefox.