It depends. I know people who have done that in a single day. You know how well you do at higher elevations with a backpack on, I hope, because it is definitely a subjective and individual thing. Food is, too. Some people subsist on a granola bar per meal, others bring full meals for every meal. You will want to be absolutely certain that your food, hygiene items, and any trash associated with either will ALL fit in the bear canister you will be carrying to keep the Bears from getting any of it.
There is no shuttle that goes from the valley to Tenaya Lake - you will need to reserve tickets for the hiker bus, if the new concessionaire continues to provide that service, or bring money for the YARTS bus that goes over Tioga Pass each day.
You need to decide when you are going - the cables do not go up until Memorial Day, usually, and later if there is still ice and snow. And Tioga Road will open when it is plowed and free of rock/tree fall, and that will be possibly June at the earliest -- but does not mean that the trails will also be free of snow. Your intending starting point will mean crossing the outlet of the lake, which can be a deep wading experience when snowmelt is going full blast. And you will need to jump, not walk, JUMP on the full trailheads page and figure out if you still have a chance at reserving permits if you do not want to chance walk in permits being unavailable -- and on that permit you will need to indicate that you want a Half Dome permit along with the wilderness permit -- for overnight trips you don't enter the same lottery as the day hikers trying to do Half Dome.
Instructions here:
http://www.nps.gov/yose/planyourvisit/wpres.htm