IBS is only a DQ if: "... of sufficient severity to require frequent intervention or prescription medication or that may reasonably be expected to interfere with military duty." (DODI 6130.03, section 5.12.c.9).
That may be pretty easy to overcome-- simply have your doctor assess whether it is so severe that you need prescription medicine or frequent intervention.
Asthma seems to be a pain, but is doable if you go off of the multitude of posts on here where people had success.
Per the same DODI, section 5.10.e: "History of airway hyper responsiveness including asthma... Symptoms suggestive of airway hyper responsiveness include but are not limited to cough, wheeze, chest tightness, dyspnea or functional exercise limitations after the 13th birthday....History of prescription or use of medication (including but not limited to inhaled or oral corticosteroids, leukotriene receptor antagonists, or any beta agonists) for airway hyper responsiveness after the 13th birthday."
The key above there is, of course, is asthmatic symptoms after the age of 13. Also, note that inhalers are only a DQ if prescribed for airway hyper responsiveness. I don't think that getting an 1-time prescription for acute bronchitis (which seems to be more common these days) would be a DQ, although it might cause some questions.
I am far from an expert, but hopefully the above two excerpts at least get you thinking in the general direction.