When you learn a rootless voicing, start out by playing it in your right hand while playing the bass note in your left hand. This will train your ear to recognize the bass note when you hear the rootless voicing. Additionally, it's really helpful to practice these rootless voicings over common progressions like the ii-V-I. Practicing over this progression will prepare your ear for tons of songs that are built on the ii-V-I. Additionally, repetition is key to training your ear, so take your ii-V-I rootless voicings through all 12 keys. This will give your ear tons of repetition, while still providing an interesting technical challenge that will keep your interest.
After finishing this in all 12 keys, switch roles: play the rootless voicing in your left hand, and play the root in your right hand. Or if you're ready for more of a challenge, do this: as you play the rootless voicings in your left hand, try playing arpeggios built off the root with your right hand. Once you can do this, try improvising lines with your right hand.
If there are specific songs you are playing with your ensemble, then practice your rootless voicings in those songs in the manner I've described above. For general-purpose practice, use ii-V-I's.
All of the suggestions I've described will help train your ear to hear the bass notes while you play rootless voicings. To that end, these techniques won't be extremely helpful to your solo chops. Ultimately, those two things are pretty different, and each requires its own practice time on skill sets that may not transfer from one setting to the other.
(Although, it is worth mentioning that, as you get better with rootless voicings, you'll find them making more and more appearance in your solo arrangements. This is a good thing! Our solo piano playing would be quite constricted and could become bland if we required every chord to contain the root.)