First of all: what is the intention of your setup? What are you trying to measure, what do you want to do with the data? Where is the bucket located, in your backyard or miles away in a forest?
I foresee some problems with your current setup.
First of all, you need a enclosure that keeps your 'duino and other components dry and at a comfortable temperature. I don't know how severe the weather conditions are, but stuff can get unreliable when used close to the min/max operating temperatures. Can you find an enclosure that can protect your electronics against the elements?
My advice: think of a good enclosure.
Second, do you really think PING))) is the best sensor? Have you already tested how it behaves around water? Are the measurements correct?
Another option would be an array of metal strips, one connected to +V or GND, the others to separate ports on your Arduino. Space them evenly from the bottom of your bucket to your maximum water level (drill a hole in the bucket to prevent overflowing or drowning your duino). Poll the pins at a predefined interval (not too short, keeping battery life in mind) to see which ones make contact with the water (allowing current to flow from/to the pins from/to +V/GND)
My advice: do some research on sensors, or try to make your own
The best way to communicate with your 'server' (what are you going to use?) totally depends on how far it is from the bucket. GSM shields are quite pricey, other alternatives may be preferable (and do not have additional phone costs).
Is your server on the other site of the window? Bluetooth? Somewhere in your backyard? Zigbee. Across the street? High-power Zigbee (if allowed by local authorities). Far away but with WIFI access? Zigbee, posting data to an online place. In the middle of nowhere but with great cell phone reception? GSM.
My advice: check out wireless communication possibilities. There's a ton of them, each with pros and cons.
Last hurdle, energy. Your battery setup will most definitely NOT be able to provide enough energy for a whole year. There's just too little juice in them.
Arduino and standalone AVRs often have a sleep mode, in which power consumption can be very very low. Google is your friend on this one. Still, that won't let your setup last a year.
Unless there was a gigantic glowing ball of plasma hanging around some 8 lightminutes from here and we could harness its incredible power with the use of photovoltaic elements... Wait, we totally can! Using (a) solar panel(s) and some simple circuitry you can recharge your batteries, and depending on the weather conditions this could keep your project up and running for a year.
My advice: get down and dirty with small solar panels.
I really appreciate your ambition. If done right, this could be quite the project for a beginner! Just make sure you thoroughly research every part of the system, on itself and as a whole. This could prevent a lot of disappointment and unnecessary costs, while only expanding your knowledge.