what does this mean? what is a bearer share company? and which jurisdictions would that be?
A bearer instrument is an instrument which states that it is owned/controlled/usable/valid for the benefit of whoever possesses it, and normally doesn't rely on registering that ownership with an authority.
https://en.wikipedia.org/wiki/Bearer_instrument
A bearer share company is a company that doesn't know or register who owns it. If, at a particular moment, you own the physical certificates that connote ownership, you own the company.
For unlinking, Monero (cryptonote technology) is the private cryptocurrency to use today. The primary different between competitors is that Monero is private by default. Other 'private cryptocurrencies' are public by default with an optional privacy gimmick (see mixers, Dash, Zcash). Transparency is the optional gimmick in cryptonote.
You want to keep a balance of Monero, and use services like Shapeshift, over TOR, to pay for invoices priced in bitcoin.
Exchanges like Kraken allow you to buy Monero directly nowadays with USD. So bitcoin isn't part of this equation anymore, the network effects supporting bitcoin's incumbency were extremely overstated.
But if that infrastructure isn't yet available in your area, buy Monero on an altcoin exhcange after buying bitcoin. Or even shapeshift Bitcoin for Monero, just to top up your balance.
This is the separation of cash and state, so don't worry about what they think, this is a parallel infrastructure that doesn't leverage their financial institutions.
so now you can email him anonymously over TOR, and pay his bitcoin invoices Shapeshifting some Monero
I also checked the Panama Papers and none of those entities they filed for me appeared in the leak, but even in the off chance they did, you wouldn't be associated.
GreenCloudVPS also takes cryptocurrency.
and finally, there is at least one jurisdiction in the world that still offers legit bearer share companies which require no registration. And your entity no longer needs a banking relationship to acquire goods and services.