What type of bond is this combination likely to form

A combination is certainly possible, but you should not take formal charges so literally

Normally, when a covalent bond is found, the two atoms both bring in one electron. As you identify correctly, in the case of nitric acid that would not be possible completely. If you draw the different possible resonance structures, the most likely structure has a single bond between the nitrogen and an oxygen where the oxygen has 3 lone pairs and both electrons in the bond are donated by the nitrogen. This makes the nitrogen "positive" and that oxygen "negative", but in fact the electrons move more freely in the molecule and charges are more distributed. You will not be able to find "the negatively charged" oxygen atom.

Explanation: