How to seamlessly upload to Strava after a ride using a Garmin Edge 500?
I personally use a Garmin Edge 810 which can connect via Bluetooth to your smartphone and then automatically upload rides to Garmin Connect. The auto-transfer from Garmin Connect then allows your ride to appear in Strava almost immediately, however, this isn't without it's short-comings. 

As per my comment on Mac's answer, I have found the auto-upload functionality very hit and miss ever since owning my 810 in April last year. Recent firmware updates have significantly improved the reliability, but it's still not perfect. Saying that, the fact it doesn't hit my phone's battery life is the winner for me.

There are lots of different devices on the market, but a quick look on Strava's own store has highlighted the Wahoo RFLKT which connects to your smart phone. Without a connection to your smart phone, the Wahoo is essentially useless. However, it would appear to be quite good as it allows a direct connection with your Strava app (displaying data that the app outputs), only costs $99 and then you have the piece of mind that your data will ultimately end up in Strava as soon as you finish your ride. This again has it's own cons as you need to use your phone as the main cycle computer, ultimately draining your battery quite rapidly.

It then really comes down to an argument of which appears more useful. A standalone bike computer with the ability to auto-upload when paired with a mobile phone, or a computer which simply displays data outputted by the Strava app at the sacrifice of your phone's battery life.

Wahoo RFLKT on the Strava store

Other alternatives on the Strava store