Just north of Konstanz, 5 km from center past OBI, there is a large 'lager' bike store ... also deals with Swiss customers, ie mwst refund.
We were there looking for a good mid range mountain bike, there was no hassle with looking and trying quite a large selection. Shop assistants very helpful.
Also large selection of road bikes, and an online shop if you want to browse. http://www.zweirad-joos.de/