From the info you supplied, the answer I have is NO... Alexa can't change the input of the Stereo... however... it may be able to once they actually start getting the new Echo Plus on the market. It has a "Hub" built in that may actually do what you are asking for the Dot to do...
Until you have either the new Echo Plus, or a Harmony hub (Or maybe a Samsung Smart things hub) you will be required to switch the input outside the Echo environment, but will be able to pair the Dot to the speaker when it is set to bluetooth. The bluetooth pairing may happen automatically when in bluetooth mode, it may not. It could require a voice command or even a computer or phone app to connect.
I use a Logitech Harmony Hub to control my audio video through Echo. It allows me to just ask it to connect to bluetooth sound bar and then I can play music or use the sound bar to audibly give me feedback from the Dot at Sound bar levels... whatever they are at the time (It's usually really loud and unbearable to work with the Dot through the sound bar).
If you can stand it for a few days or weeks, until the Echo Plus comes out, you may be able to upgrade to it selling your dot and buying the new model, albeit more expensive... But we are none sure what the complete functionality is available through it yet... Also, for less money, you can go on Best Buy.com and buy a Harmony hub for 89.99, and they will give you a penny back and they will throw in a Dot so you could have one in another room as well if you choose well in their Harmony listings. (See Link below for the Best buy listings)
https://www.bestbuy.com/site/searchpage.jsp?st=Harmony+Hub&_dyncharset=UTF-8&id=pcat17071&type=page&sc=Global&cp=1&nrp=&sp=&qp=&list=n&af=true&iht=y&usc=All+Categories&ks=960&keys=keys