UVB-76 is definitely a shortwave oddity, but not really a numbers station; it's more of a marker, beacon or pilot. It is not necessarily known to broadcast messages on a regular basis, though strange messages have been heard from it.
True numbers stations, on the other hand, exist for the purpose of transmitting encoded messages with regularity and there are a great variety of these types of stations. Some are voice, some are CW (morse code) and some yet might be other modes. A lot of work has gone into identifying the regularity and schedule of these transmissions and you can find some of that information here in our Numbers forum, or on #wunclub on IRC, or from a number of other resources.
Your SDR-Radio software, as you know, lets you connect to various internet-enabled radios where you can, from there, control the radio (tuning, mode, etc). Hearing UVB-76 (or any other signal) from these radios will vary widely, with propagation and time of day at the location of the remote receiver being the most significant variables. UVB-76 broadcasts at 4625 KHz. I'm assuming you are in one of the North American timezones and so in all likelihood you would be listening in the late afternoon or evening. Connecting to a remote receiver located in Europe might be your best bet for hearing UVB-76, though at times and depending on propagation a North American based receiver might hear this reasonably well, too.
Incidently, a VERY good European based SDR is available on the web at:
http://websdr.ewi.utwente.nl:8901/The beauty of this receiver is that you do not need any special software... just a web browser with a Java plugin, which is fairly universal. I just connected to it (at about 1:30 PM Eastern time) and punched in 4625 KHz (also, switch the mode to AM) and sure enough, there is UVB-76 in all of its buzzing glory. By contrast, I am unable to hear this signal on the receivers that sit here on my desk, connected to large outdoor antennas. This is a (predictable) consequence of propagation. Signals on this frequency, transmitting from Europe during daylight in North America, are unlikely to be heard here. However, since it is likely dusk or dark in the Netherlands, where this receiver is located, I can hear it well using a remote receiver located there.
I'd expect to possibly hear this signal on my own receivers when nightfall reaches the east coast (I'm in Boston).
I hope this was helpful, and others are sure to chime in.