Ok. Tried using a 1/8" to 1/4" cable to plug my ipad/iRig into the input on my amp - sounded ruddy horrible. Like the speaker was under water.
Running an amp sim into the front of your amp won't sound great. You've got a simulated amp feeding into simulations of a bass cab and a mic. Then you're cabling that out of your iPad and over to your amp, which already has a bass preamp, a power stage, and a regular bass cab. That's like putting a mic on an SVT, then daisy chaining it into another SVT...
Still, it shouldn't sound THAT bad, if you've set everything accordingly.
First, play a regular mp3 of full-range music on your iPad, and run it straight out of the headphone jack, through your adapter cable and into the instrument input on your amp.
Now adjust the EQ on your amp, until the music sounds as normal as you can get it. Hopefully, the result won't be too far from running it into a home stereo or a good boombox. On most bass amps, that means turning off the "slap" or "contour" controls, rolling off some bass and treble a bit, and then pushing the mids.
When you've got it as good as it will go, then re-connect your iRig, and try using JamUp/Amplitube/Pocket GK/Whatever.
Because you've still got the simulated amp and cab in series with your real amp, it will likely sound a bit flabby on the low end, and there may be some extra hiss.
But sound like it's underwater? No way.
Assuming your amp has an effects return or an Aux jack, then the next step would be to send the iRig output into there. This should tighten up the sound some more, and hopefully give as much output with less hiss.