If your amp doesn't have line-out, a DI box or an interface with an insturment input is probably your best (most economical) option. If you really want to keep the cost down, Behringer makes a guitar-USB interface for about $40 USD and I assume it would work on bass.
Or, you can stick an SM57 in front of your cabinet.
They are expensive, but you can get an
attenuator that knocks-down the signal while putting an 8 or 16-Ohm load on the amp to retain the sound characteristics of your amp.