There are many SMS gateways out there that offer differing levels of service, and that would be the option I would recommend for a commercial venture of this size. If you need to scale above the turnaround they can offer, then you probably want to speak to the mobile carriers in your region, who should be able to offer a direct link to their network and you should be able to send and receive insane numbers of SMS messages (last time I looked into this, said networks were all based around ATM).
The alternatives if you want to start small would be to use either a dedicated GSM modem, and handle it that way, or even use a Windows Mobile, and develop your own message interceptor for that -- these options would be better suited to something of the scale of a taxi company or a takeaway, rather than a bank though...