Hi,
To give a phycist's point of view: Photobleaching is a quite complex process and oxydative attack is just of the possible pathways for it, although one that is fairly common in biological samples.
From the physical perspective, a molecule's stability is defined in terms of energy. To radically simplify it, think of all the possible chemical structures of the molecule and its close neighbours as a landscape: The elevation represents chemical energy, X and Y coordinates represent "chemical structure". Of course there are actually N coordinates involved, with N the rather large number we arrive at by taking three for every atom and substracting translation, rotation, and perhaps internal changes that we still choose to call the same molecule, such as rotations around bonds. The human mind is more comfortable with just two coordinates. Stable molecules are represented by valleys in the landscape, where the depth of the valley below "sea level" is the binding energy of the molecule. There may be a few "mountain passes" allowing transit to different chemical configurations by a simpler way than taking the entire molecule apart and rebuilding it from scratch.
Now if we look at the electronic states, the ground state of a stable molecule is near the bottom of the valley of chemical energy -- not at the bottom, for quantum-mechanical reasons, but still quite low in it. It is like a trapped cloud bank. Perhaps a nearby valley, representing a reaction with a nearby oxygen molecule, is deeper, but there is no easy way of getting there. The change in chemical structure can only be achieved by crossing a high barrier, the height of which is the "activation energy" of that reaction. The probability of crossing the barrier decreases exponentially with its height, making it an unlikely event. Unless you can put in extra energy, for example in the form of light -- something chemists do all the time when they perform photochemistry.
The singlet excited state has an extra amount of energy that is, in chemical terms, significant. A 488 nm photon has 2.54 eV of energy; the binding energy of for example a C-C single bond is 3.6 eV. So the corresponding "cloud bank" sits higher in the valley. For a normal fluorophore it is still trapped, surrounded by energy barriers, but from the new perspective these are a lot lower. Getting over that barrier is now much more likely than for the ground state, and the excited state may be metastable rather than stable. However, for the singlet excited state there is another event that is still much more likely, at that is fast return to the ground state. The two processes compete for the fate of the excited molecule, and that makes the chemical reaction a relatively rare event, which will only happen in significant amounts if you try often enough.
The triplet excited state, to be of importance, actually has to be lower in energy than the singlet state. From the perspective of the triplet state, the energy barriers are a bit higher than for the singlet state, and therefore a chemical reaction may actually be in itself, per time unit, less likely. (Various quantum-mechanical selection rules and interactions make it more complicated than that.) But for the triplet state, the probability of the competing process of return to the ground state has shrunk into insignificance, becoming anything up to a few billion times less likely. Because the two processes still compete for the fate of the molecule, the odds that it will react are a lot better.
However, virtually eliminating the return to ground state improves the odds for /any/ process that can interact with an excited state. Oxydation is not the only process that can happen, and not the only one that can cause photobleaching. For example, excited states can also absorb light, with a different absorption spectrum than the ground state. Light might be present at the same wavelength as the original excitation or, if you use multiple lasers or a multiband excitation filter, at a different one. The additional energy supplied by that light may be enough to permit a different chemical reaction, perhaps through ionisation. On the other hand, the photo-excitation of a triplet state to another triplet state may finally allow the molecule to return to a singlet state, followed by a rapid return to the ground state, thus actually reducing the probability of photobleaching. Feedback loops like that probably make the dependency of photobleaching on intensity, exposure time, and wavelength so complicated.
Best Regards,
Emmanuel