I think about an hour one to the other on a coach. Their are lots of travel agencies offering evening shopping trips into the town for a few euros, so hopping on one is easy enough. It's cooler by evening, and nice to sit out having drinks too.

There is good shopping both in the old part of town down lots of twisty, narrow streets (plenty of leather goods, ceramics, jewellery shopping, and also in the less touristy area where the main shopping (clothes/fashion) area is.

The more touristy area has shopping til late evening, where as the main area where local people shop has more standard opening hours.

http://www.corfunet.com/corfu/corfutown/shopping.php?PHPSESSID=8e2454e3c6e15772ad00466ff7dcf2f0

Some good shopping experiences recounted here
http://www.virtualtourist.com/travel/Europe/Greece/Prefecture_of_Kerkyra_Corfu/Kerkyra-423234/Shopping-Kerkyra-BR-1.html

There is a local bus service between Sidari and Corfu Town however it goes the long way via Roda and Kassiopi, so probably takes at least an hour and a half. Much better to go by boat. Just check the local agents.

As to the shopping, if that's your therapy, you will be in heaven.