Depends on your buffer size, bandwidth, and what you're demodulating/decoding, but it's pretty fast. With a narrow bandwidth on a fast port and simple modulation/encoding, maybe a few milliseconds?
Counter-intuitively, it is often difficult to reach low latency with "narrow bandwidth" (you mean low sampling rate), because many SDR interfaces are designed to fill full packets with data, not send tiny packets (ex: Ethernet packets). This problem goes away above 1-10Msps.