Not an unusual problem with disposable pipettes and organic solvents, and is worse with low boiling solvents such as ether and acetone. This is largely due to the vapour pressure of the solvent at room temperature and the low surface tension. A tip is to keep the solvent cold.
These are also a pain with viscous solvents or polymer solutions because there is not enough 'suck' in the bulb because the capillary at the entrance to the pipette is too narrow. The trick here is to break off the tip to give a wider entrance to the pipette. The wider tube will give a lower pressure drop (Darcy's Law?).
I tend to draw my own disposable pipettes then I have control over the capillary at the tip.
If you want a measured volume, without going to the expense of an autopipette, then glass serological pipettes are useful. Another alternative are glass syringes.
A problem with using cotton wool is that the solvent may remove the oils in the wool and this contaminates the sample.
Some organic solvents will remove the plastizer from plastic pipettes, so while the pipette may not 'dissolve', the solvent may be contaminated with the plastizer.
In the end it depends on what you are using the solvent for.
Hope this helps.