I found this thread recently while Googling how to do this myself. So, although this is an old thread, it does pop up on Google if searching for this stuff, and it is actually one of the more useful. So I though I would add this.
I have put together a system that gets pretty good sound. I have used it for a couple months now. I have no opinion yet on the longevity of any of the components, but they have handled rain, cold, and direct sun well so far.
I use a wired (not battery-powered) waterproof microphone, a tiny Bluetooth transmitter (battery with USB charging), and a bluetooth speaker (also battery/USB charged). The microphone I got from Amazon for $28. The tiny Bluetooth transmitter/receiver I got from Ebay for ~$9, but is also available from Walmart. It is about 60% of the size of a saltine cracker. The Bluetooth speaker I got at Staples clearance for $16. This speaker is normally way more expensive, but I think that many $10-$20 Bluetooth speakers would work just as well. I am not sure how well other microphones would work. The transmitter is so cheap that I would not really worry about using a different one.
I use a Bluetooth setup instead of wiring the microphone to the speaker because the access point to run the microphone wire outside is a floor up from where I want the speaker. The one challenge is getting the speaker and transmitter to pair up via Bluetooth, but eventually I always get it to work. I have not yet figured out the exact sequence of steps that these two prefer to link up, so I just punch buttons and curse until they cooperate.
The microphone comes with a very long extension wire. Although my arrangement is such that the extension is unnecessary, I use it anyway. I could mount the microphone 50 feet further away if I needed.
As for sound quality, there is a bit of hum if I turn the speaker volume way up. I no longer notice any hum, although if I concentrate there still is some. I found that there is actually a continuous small amount of sound from nature itself. This rig is every bit as sensitive as I had hoped for. It clearly picks up soft bird noises and turkey scratching 50 feet away (also backup beepers a half mile away and house siding sun expansion pops). There is an odd fraction of a second delay in the sound, but that is generally inconsequential. Also, gusts of wind make typical microphone noises. I put a piece of A/C filter over the microphone and it reduced the wind noise, but not completely. I am now quite aware of when it is windy or rainy outside. I have not used this yet in the winter, but I bet it will pick up the sound of a decent snow falling. Thunder commands attention. I also notice that the sound makes me feel like a window is open and I unconsciously sense a draft, sometimes even feeling cold (a mind is a curious thing). It also picks up noises from inside the house, so beware if you swear or fight a lot.
Because of the hum, I got a small audio mixer to adjust the signal, but I found it to be unnecessary.
Googling "waterproof microphone" and "bluetooth transmitter receiver" gets plenty of hits for these parts.
Details of the components are:
Microphone
"Tonton High Sensitive Weatherproof Preamp Microphone Audio Pickup Device Sound Voice Pickup Kit with 60 Feet Cable and Power Supply for CCTV Surveillance Camera System"
Bluetooth transmitter/receiver
"Bluetooth 5.0 Audio Transmitter Receiver Adapter, Bluetooth Transmitter for Car 2-in-1 Wireless 3.5mm Low Latency Stereo Audio Adapter for Home Sound System/TV/PC/Tablet/Speaker Headphone"
Bluetooth Speaker
"Altec-Lansing Mini Lifejacket Jolt with Lights"
alteclansingsupport.com
Other
A cable/adapter to convert the microphone's RCA male output to the transmitter/receiver's 3.5mm audio input. These are less than $5 from a host of sources. Usually these are stereo (2 RCA plugs); since the mic is mono, I only connect one of the RCA plugs.
I hopes this helps someone. It took me a bit to figure out, but it is not hard.