Unfortunately this is probably not possible. The only way to send Bitcoins is with the work of miners. They use their resources such as computer hardware and electricity to do the mining and therefore they get paid for that effort. There's no way to avoid that with Bitcoin as far as I know.

However, there is an alternative. I'm not trying to promote another coin on this topic, but to fully answer your question, IOTA doesn't charge fees for sending coins. It's built into their architecture that as you send coins, you mine for 2 other transactions so everyone shares in the mining equally. The point is that if you don't want to pay a fee, you may want to consider sending IOTA rather than Bitcoin.