The main providers are BITEL (0502), KATEL (0517) and FONEX, the most recent company to operate in Bishkek. BITEL operates on the GSM system, so you may be able to use a roaming service and your own number.
Local SIM cards may be bought relatively cheaply from many outlets in the city, especially the third floor of TsUM. Both BITEL and KATEL provide a service that does not entail setting up a local account. This works by purchasing a SIM card with a local number and a card with credits (Mobicard for BITEL, K-plus for KATEL). When your credit is exhausted you will need to buy another card and dial the service provider and enter a serial number, which will add the new credits to your account.