Bug Repellent for Mountain Biking that won't melt my gear? The east coast is supposed to have a really bad year for ticks with Lyme disease as well as the concern about Zika Virus and West Nile Virus. 

I know DEET is effective at both keeping bugs off and melting technical gear. I'm worried that repeated use of DEET will destroy my nice Goretex jacket, my expensive bib shorts, my softshell trousers, synthetic jerseys, and technical overshorts. 

What's the best option for repelling mosquitoes and ticks for mountain bikers riding in the woods that won't harm my technical gear? 

See Example:
http://sectionhiker.com/deet-dissolves-breathable-fabrics-experimental-results/
https://www.outdoors.org/articles/amc-outdoors/two-common-hiking-items-that-deet-will/
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.