Left click on the "Search" link near the top of the page, and immediately click on "Advanced Search" at the bottom of the menu that you'll see.
Under "Keywords" type in "silicone Manitoba snow" without the quotes.
Under "Username" type in Nestor_Kelebay
Uncheck "Search Children's Forums" at the bottom of the page.
Now click on the "Search Now" button also at the bottom of the search page.
You should see a thread entitled "bathtub caulk".
If you read and understand what I posted in that thread, you'll know more about working with silicone caulk than 95% of the "experts" answering questions in internet DIY Q&A forums like this one, and will be well prepared to replace the silicone caulk around your tub.
However, before replacing any caulk, check the obvious things. Remove the knobs and tub spout from the plumbing and check for the possibility of water leaking through the wall penetrations. If you see places water can get into the wall around the knobs or tub spout, fix those leaks before you start suspecting the silicone caulk.
Your water valve handle is probably just stripped. However, if the house is new to you, it's possible that that shut off valve leaks, and the handle was stripped by the previous owner twisting the bygeezus out of the handle trying to shut off the water flow completely. One of the best investments you can make in your house is to replace this valve (if it's leaking) with a ball valve (which is the most reliable valve you can get). That way, you can always shut off the water flow to the house completely in order to do any plumbing repairs.
Also, not all ball valves are made equal. Some companies are making ball valves that don't have a packing nut. Make sure the ball valve the plumber installs has a packing nut. Alternatively, buy a ball valve of the correct size (based on the size of the water supply piping the valve has to go on) and ask the plumber to install it.
In the image of the ball valve above:
Look under the handle of the ball valve, and you will see a hexagonal nut. That is the valve's packing nut. If water ever starts to leak out of the valve past the shaft the handle turns, you can stop that leak by tightening that packing nut a bit. The packing nut is never supposed to be TIGHT like a screw or bolt is tightened; it's just supposed to be tight enough to prevent water from leaking past the shaft the valve handle turns. Tightening the packing nut more than is sufficient to prevent water leakage will simply result in the packing wearing out prematurely, necessitating the replacement of the valve.
With ALL ball valves of the type shown above, the valve is open when the handle is parallel to the valve body and closed when the handle is perpendicular to the valve body. The valve shown is meant to be threaded onto iron pipe, but you can get these kinds of valves that are meant to be soldered onto copper pipe. The valves meant for being soldered onto copper pipe are intended to be soldered without taking the valve apart. The teflon seals inside the valve will tolerate the high soldering temperatures as long as the plumber takes care to ensure that the valve is in the OPEN position when it's being soldered into place. (I like to remove the handles from ball valves when soldering them in just to ensure I don't scorch the plastic on the handle with the torch.)