I have a couple of options for silent practice myself:
1 - Darkglass A/O Photon (or really any of their Ultra or Photon/ADAM type pedals). I love that it gives me all kinds of options for tone/sound/eq, the headphone out is great, it's a DI that can be used as an audio interface into my laptop, it has cab sim, and I could go on and on about how great it is. Only downside is price, and the fact that it is mounted on my pedal board (for gigs and band practice) and I don't want to dig that out and set it up each time I just want a headphone option.
2 - Zoom B1X. I LOVE this pedal. I have had more than a couple zoom multi-effects pedals and for what they are and what they cost they're hard to beat. Not all of the effects sound excellent, but the ones I use regularly sound fine. For practice, it's hard to beat. Plug in bass, plug in headphones and play. It's got a built-in drum machine and metronome which is decent, built-in tuner, looper, headphone volume control, and SO many other features. It's also super user friendly. As much as I love the DG A/O Photon, I find the Zoom pedal to be more convenient and as a result of that it's become one of my main practice tools. (I even use it regularly plugged into my practice amp to practice with volume).
My practice amp is a small Ampeg, and it has a headphone out that I use sometimes as well, but it's hard to beat the convenience and portability of the zoom pedal so it is my go-to.