An extremely simple yet capable compressor circuit is published by Elliott Sound Products,here (link updated 31 Dec 2023).

Compressor Mk I

I built the circuit exactly as-is (in an Altoids tin).

Care was taken to optically couple the bulb to the photocell (LDR), using a perspex rod, wrapped in smooth tin-foil.  The perspex came from eBay: http://stores.ebay.co.uk/thewholesaleposco2009

as did the miniature “Grain of Wheat” bulbs:  http://stores.ebay.co.uk/GnA-MODELPARTS?_trksid=p2047675.l2563

This was put together, and sealed in heatshrink tubing, to make it fairly lightproof from external light sources.  The rest of the components came from http://cpc.farnell.com (free postage) or from my junk box.

I have an Ashdown Little Giant amp.  Several reviewers have mentioned that this amp is not at loud as it should be (e.g. here).

It all depends on whether the output levels coming from your bass are enough to drive the output stage fully.  I have an active bass, but even with the input set on max, to get a decent output level I need the output volume control set to around 3 o’clock.