As others mention, get some nice headphones first. As I'm feeling too much sound pressure with over-the-ears headphones when playing bass guitar, I'm now using in-ear and I'm having as much fun with those than playing my main rig. I have Shure E-2, which are far from the best, but since they are a bit "bass heavy" they work very well for our application (tons of bass!!!!). Just remember with in-ear the tighter the seal the better the bass response and the sound overall.
If you will use a passive bass you may have to go first into a preamp pedal or a DI when using a small mixer. Might not be a problem with an active bass, but even than you better test first.
I've used iRig with Amplitube and PocketGK, sounds ok but far from good.
I'm currently using Line6 Toneport GX which comes with Pod Farm (5 bass amp models). Sounds really, really good (I can send you some presets of Ampeg SVT, GK800RB and Eden Traveler amps if you want).
Honestly I think the MB200 (or TC BH250) is the best option. You can use it for silent practice, you can use it for recording with the DI, you can pair it with a 1x10 or a 1x12 for home practice or for acoustic gigs, you can use it as a preamp/DI for direct FOH or rehearsal and you can even add a second 1x12 (or your current cab) for small/medium gigs. Way more options that iPhone/small mixer IMO.