I'm not sure if I am allowed to link it here because OCUK sell similar things but are you talking about something with 16GB of RAM and 512GB of SSD for £140?I'd grab a cheap as chips n100 or n105 minipc and install FreeBSD on it. Otherwise you're generally going to be having to spend a decent amount to run something bare metal, bear in mind most providers like Vultr who have a FreeBSD offering are running it via a virtualisation layer which is never gonna be amazing, unless you go for bare metal which is extremely costly. N100 won't take up any more space, is pretty much silent and will run Bhyve perfectly. Case in point, it's running in my homelab at the moment.
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