When I get into the car and power it up, I find that it takes upwards of 40 seconds for the car to reconnect to my phone via Bluetooth. My testing conditions were that I had music streaming via Bluetooth off of the iPhone when I turned the car off, so the car defaults back to the last audio device, which was the iPhone. If I'm not streaming music, I might get a connection established to the iPhone in about 25 or 30 seconds if I left it on the phone screen. I have the Base model. Is the Advanced model any faster? The reason I ask is because the Highlander Hybrid we're getting reconnects to the phone in less than 15 seconds for playback of music. I didn't test startup time for just a phone call, but will do that shortly. Another nice feature of the Highlander's audio system is that I can fully browse the iPhone's playlists, artists, albums, etc, via Bluetooth, whereas on my Display Audio unit, you have to plug the phone in to do so.
I think my 2012 base is similar to yours with regards to connection time - around 40 seconds. I generally keep BT off on the phone and use my earbuds unless my wife is in the car and then I'll turn on BT to use Pandora.
I keep Bluetooth on all the time on my phone. I constantly am streaming music from the phone's library, and the phone is also a data hotspot so the car gets traffic and other data services (fuel prices, weather, etc). Not to mention being able to get phone calls using the hands free speaker system. In my state, it's illegal to drive with headphones on, or anything that would block sound from entering your ears, so earbuds are pretty much out as well, unless you use only one ear. And a hands free law for using the phone in the car.