Bug Repellent for Mountain Biking that won't melt my gear?
Check if icaridin (Wikipedia) protects against disease vectors in the region you would like to bike at. 

Icaridin is less damaging to synthetic materials, less sticky, and repels many types of insects (and arthropods).

Icaridin also has down sides, for example, it may not be adequate for some disease vectors and a single application does not protect as long as DEET does.

Please note, that these draw-backs are particular relevant for 7% solution of icaridin. Most comparative tests that find an equivalent effectiveness of Icaridin to DEET use a 20% solution. The latter may not be available as a commercial product in your country.

The topic effectiveness of insect repellents is also covered on (travel) stack exchange.