Can I just add,in addition to the EHX I use the Vox AP2-CL headphone amp, it’s designed for guitar, but has a clean channel,Fender Bassman (which is actually quite good for bass), and an overdrive channel (less useful). It has a gain control, tone (essentially a LPF) and a volume control.
it also has chorus,delay and reverb effects,and of course the line in for iPods etc… of the ‘amp sim’ headphone units I’ve tried this has been the most useful, but still quite plasticky.