Emulating BIOS itself is not that hard. You can probably hack DOSBox to run AMI 386 or 486 BIOS but it is not going to do much -- the main function of BIOS is to initialize and autotest all kinds of hardware, quite often at the lowest level. The emulated hardware is quite different so it is not going to work. Most BIOSes will probably fail really early right after checking mobo/chipset type or revision. Emulating hardware at level that low is tricky and practically pointless as it does not improve compatibility. The number of different PC hardware would make this project about the same scale as MAME if not larger, with much lesser benefits.
The closest you can get right now is PC emulation in MESS but it covers only four (iirc) very old IBM BIOSes and I don't think it will get more features in that part any time soon.
That said, here's an interesting idea for DOSBox configuration frontend -- to make it looking like old school AMI or Award BIOS setup 😉