Hi gwt
Personally I wouldn’t bother writing. Most farmers don’t have the time or inclination to proactively respond to unsolicited mail, however polite the intention.
Find the location and knock on a few doors to find who owns the land. Most locals will have an idea and probably some indication whether the approach will be welcomed or not. Then call them and explain what you are looking for (need and frequency of access etc) and offer to come and meet them, if they would like. You can but ask. Don’t be too offended or disheartened if they just say no. It won’t be personal, just they may not want the hassle of sorting it out and it’s often easier to just say No. Others will be fine with it.
If they are up for it, after I had met them and agreed a suitable spot I would personally offer a written undertaking of what you will and will not do, including (not necessarily labouring the point, but mentioning it) ensuring you retain ownership of the kit and any honey, and rental you are prepared to offer for their trouble. Traditionally that is an annual jar of honey per hive and always seems appreciated.
Most people don’t bother with the latter part and it’s all good for a shake of hands for years. But some out apiary arrangements between strangers can go sour for the weirdest of reasons and you both should be clear from the outset what you can expect from the arrangement. Good luck!