As a New England hard-snow skier who has been working on and improving my bump skiing these last years, I'll disagree with many here. You can get a good groomer ski, then improve your bump skiing technique so you can make that ski work there.
...it does seem like a bit of conflicting goals regarding a carver/groomer and a mogul ski. So I would probably use this ski about 70-75% on groomers/carving and 25-30% moguls.
You're doing several things right. 20 days a year is decent, and getting those 20 days in concentrated consecutive days is good also. Since good bump skiing is merely good skiing in 3D, there's a lot you can do on your frontside skis to make you better in the bumps:
Learn how to finish the turn in balance, poised like a coiled snake, ready to strike the next turn.
Learn how to snap off turns quickly. Like one per second. One thousand-one, turn the other way. One thousand two, turn the other way. 20 times in a row.
Work both feet independently. If you have a weak foot/side, strengthen it.
Make sure you are flexing in the turn. Learn to ski like a slinky, not a board.
Focus your lessons on this list. Notice there is nothing here that dictates any ski type what-so-ever.
Now think about moguls. There are moguls, and then there are
MoGuLs. The bigger they are, the more pronounced and important all your technique, line choice, and ski choice will matter. At the introductory stages and at slower speeds, less so.
Everyone skis moguls differently. The ski they choose reflects those their personal style. In general, the stiffer ski bump skiers are arcing around the shoulder of the bump. A deep trough on an I-beam will throw you, or at the least be a very jarring ride. Softer skis will buck you less in a deep trough. Many beginning bump skiers pivot and skid their way down. This is the bumps for Boomers curriculum. You might like more torsional stiffness for that.
My advice is to concentrate on the basics on your present skis, hold off on a second pair, and demo occasionally to see what feels better as you progress.