Some of my colleagues wish to do a lab in which we heat sugar vs. salt. Of course, the sugar combusts, and the salt doesn't. The explanation we will give is that the ionic bonds of salt are stronger than the covalent sugar-but this confilicts with the fact that salt dissociates in water and sugar doesn't. Please help!!

Ionic bonds are not "stronger" or "weaker" than covalent bonds. They're just different. You could just as well use freon (CF₂Cl₂) as an example: it won't burn, so covalent bonds are "as strong as" ionic bonds.

What you need to look at is the overall thermodynamics of any reaction, including combustion. In one case, the possible products are less stable than the reactants; in the other, they are more stable.

4NaCl + 3O₂ ® 2Na₂O + 4ClO

The fact that sodium chloride won't burn is a function of the fact that chlorine oxides (ClO and ClO₂) are not terribly stable beasts; chlorine is MUCH happer in sodium choride. The overall energy of the reaction is +72.5 kcal/mol of salt (+1.2 kcal/g), and we wouldn't expect sodium chloride to burn very easily!

C₁₂H₂₂O₁₁ + 12O₂ ® 12CO₂ + 11H₂O

Here, sucrose--generally considered a high-energy compound--is converted into the highly-oxidized compounds, carbon dioxide and water. The overall energy of this reaction is -1349 kcal/mol of sucrose (-4 kcal/g), and we expect sucrose to burn well once it's kindled.

On the other hand, your second example (dissociation in solution) is a function of ionic compounds as a class but not of covalent ones. Here, ions need to be surrounded by opposite charges to be comfortable, and since water can do that, ionic compounds dissociate in water. Covalent compounds (except for molecular ions like nitrate or phosphate) aren't composed of independent, electrically charged subunits and therefore don't dissociate. But again, this is a matter of thermodynamics! Salt dissolves because it's at least as stable in solution as in the crystal; calcium carbonate doesn't dissolve well because it's more stable in the crystal than in solution.

Thermodynamic data used in this answer were taken from the NIST Chemistry WebBook.