You don't need an oscilloscope at all. What you need is either a logic analyzer (if possible with a USB protocol decoder) or a standalone USB protocol analyzer.
Good thing is that oscilloscopes are rather expensive, whereas a logic analyzer that's fast enough for a meagre 1.5 Mbd/s would actually cost you less than 10$ (FX2 eval boards + sigrok software).
Chances are you don't even need that. With a normal operating system (e.g. Linux) and common software tools (e.g. Wireshark) you can capture USB traffic at the packet level in software if it happens with your computer.