How to take full ownership of an IP address?

You need to apply and be granted your own IP allocation by your local registry like RIPE or APNIC.

They require annual fees, and you need to justify your requirement (yours is legit). They will assign you an Autonomous System number and a range of IP addresses.

You must then find people to peer with (in a datacenter usually), preferably more than one. You then publish your BGP routes using your AS provided with your IPs via your new peer links.

You also should allocate a DNS server to provide PTR records for your allocation.

None of it is cheap, it requires expensive subscriptions, expensive peer links, expensive hardware (routers to do the BGP peering) and a fair amount of networking knowledge.

What I suggest is that you hire a contractor to set up the initial network and peering and firewall, etc to take the pressure off you having to learn and maintain it all, so you can concentrate on... Whatever it is that you host.

Who said that "bulletproof hosting" is expensive?

PRQ, the company that hosts thepiratebay.org, offers dedicated servers for less than $200 a month and simple web hosting for $10 a month.

From their website:

Refugee hosting
Our boundless commitment to free speech has been tested and proven over and over again. If it is legal in Sweden, we will host it, and will keep it up regardless of any pressure to take it down.

Confidentiality
We defend your integrity to the end. With our discreet customer relations policy we don't even have to know who you are, and if we do, we will keep that knowledge strictly confidential.

According to the wikipedia page they're hosting websites that promote paedophilia, so it should be no problem for them to host whatever you need hosted.

EDIT according to the same wikipedia page, PRQ also hosts wikileaks itself.