You don't need bees to pollinate tomatoes - if they are growing up a string just tap the string with a stick so the plant and the flowers shakes a bit. This is all you need do. Chillies can be hand pollinated, either with a brush or remove a flower and use that - rubbing it from flower to flower.
The problem is honey bees don't really like greenhouses unless there are a lot of very attractive flowers in there for them, and a few tomatoes or chillies, even in a big greenhouse, would not really get them very excited. Most honey bees which flew in would probably spend most of their time hitting the glass trying to get out.
Try a TBH if you want, but try and find someone locally using one so you can try before buying so to speak and you will have someone to turn to for advice. The "natural" bit about TBH is somewhat exaggerated. You can get the same effect with a conventional hive giving them a starter strip in the frame rather than an entire sheet of foundation. But TBH are generally a lot cheaper than conventional hives - which is a big plus
