Either an Aguilar Tonehammer, VT Bass, or Le Bass as a preamp, into a PJB Bighead, into Beyerdynamic DT-770 Pros. (Tried the PJB cans as well but they are harsher up top and don't have the powerful lows of the Beyers). I hardly ever plug into my amp at home these days!
The PJB Bighead is a great headphone amp, others I've tried like Zoom units are either noisy or don't put out enough volume (through my cans at least, they are 80 ohms which is higher than typical consumer headphones). I like the fact it's separate so I can plug in different preamps at will - the Aguilar gets chosen for classic P Bass and flats type of tones, and the Le Bass for modern aggressive sounds, and the VT can actually cover both.