Device is called ultrasonic transducer and it's freely available on a market.
For communications you will need MFSK modem
http://acomms.whoi.edu/umodem/
http://cseweb.ucsd.edu/~kastner/papers/oceans10-low_cost_modem.pdf
or write your own protocol and software.
Note that communication will be short range, if it's ROV and you don't consider it to be AUV it's better to use simple Ethernet cable.
Military submarines also use for underwater communications ELF, VLF radiowaves, so you might also consider this option for AUV, but data rate is very low on this type of systems.
There are a numbers of satellite transceivers, as PCB modules (size of a few coins) or boxed-product, that are low power, easy setting up and come with driver library example code.
Some low-speed equipment is not especially expensive, however, there are data volume charge which may be acceptable if you only send small data once every day.
Two types, those use LEO (Iridium and similar) does not demand very open sky view as sat is high elevation angles. Those use geo stationary sat (Inmarsat and similar) need open sky toward 'generally south', depending on Latitude.
These sat have high, medium and low speed units. Low speed, non-voice units are what you need in terms of cost, easy setting up, low power etc.
SBD Short Burst Data Satellite module
Another similar unit from another brand and service provider
For the ham path, you can use PSK31 HF modem which allows low speed (31 bauds) transmission with small antenna and easy setup than traditional HF modems of higher speed (few kilo BPS). Wiki on PSK31
Ham band need
a) knowledge to choose different freq depending on day, night, seasons, latitudes and solar cycle
b) depends on countries, may not be full legal for machine-to-machine communication not carrying 'ham traffic' (some country defined as self-training activities)
OR, can get a commercial license and use HF band (not sure how hard it is) and same ham equipment
OR use the HF network (fee based or not, 100% sure) for file and email for small yacht at sea. Check SailMail or similar
Best Answer
RF signals are attenuated greatly by water, Very low frequency (VLF) is used for submarine communications but requires a huge antenna system. Therefore Bluetooth and other RF-based systems won't be suitable.
For a depth of 30 meters accoustic modems are a practical solution. I've done some software programming for a system that used a AquaComm: Underwater wireless modem and it has an RS232 port and simple to use commands. From memory the board and transducer combined would have taken up an area of around 100 x 100 x 200mm, so I'm not sure if that would meet your definition of "small" or not.
Optical communications would be another possibility, although the only shipping commercial products I could find had a much shorter range. I found an interesting paper Using Optical Communication for Remote Underwater Robot Operation where they reported 30 meters over the length of a pool, although that dropped to around 9 meters in a harbor. With optical it would depend a lot on the water quality and ambient light.
Because it sounds like your device is always tethered by a rope the simplest and cheapest and easiest way might be to replace the rope with a cable. Assuming there aren't any dire consequences to the sensor failing and long-term reliability isn't an issue maybe standard mains cable would do the job if properly sealed at each end. It sounds like this setup it for some form of experiment?
As mentioned in a comment at that depth keeping your device watertight won't be easy so generally keeping the underwater component of the system as small as possible and removing the need for battery access will make it easier. For the same reason it might also be worth considering leaving the Arduino above water and just place the sensor(s) underwater if possible.