2005 honda recon is smoking? blue smoke....?

Sounds like it needs the top end freshened up. It's pretty easy to do because they're push-rod, so you don't have to mess with cams. Take your head and cylinder off, if the bore's in specs hone it out, get a piston kit (I wouldn't just replace the rings, I'd go all the way) + top end gasket kit off eBay, should be all you'll need. Snorkeling it with a good filter shouldn't have done it, probably just too much run time on it, not enough filter cleaning and oil changes. It's really easy to do on the OHV Hondas, once you do it, it's no problem all at the next time. You might need a Clymer repair manual, best $20 you'll ever spend. If you don't have much experience and were set on taking it to a shop, nothing wrong with that, but if you've worked on small engines before. you've got the tools and don't mind tinkering, you could save a lot of money doing it yourself. Good luck!

If you value the bike do not ride it in this condition.

There are a number of reasons why it is burning oil and none of them are good.

Find out the problem, have it fixed.

Maybe that is right