The problem is, if your sodium acetylsalicylate (called sodium AS from here on in) was to not dissolve, it would remain as crystals. Now, the crystals have strong ionic bonds between them, that is true.
However, when the crystal breaks up, there is a lot of energy released by the hydration of sodium cations (your ion-dipole bonds mentioned). Ion dipole bonds are only really meaningful when the crystal has dissolved in water (in the solid form, sure, the sodium cations may attract the oxygens, but the AS anion will repel the oxygens; it gets trippy) as then, each ion can form bonds to multiple water molecules. Sodium, for instance, bonds to six water molecules when dissolved. That's a lot of energy. I'm not exactly sure how many the AS forms.