BungeeBones offers a competitive bidding arrangement for the advertisers to move their link listing ahead of the other advertisers. So the short answer is that you 1) pre-load your account using Bitcoin and then 2) Purchase the position on the link display page you want for the offered price.
To preload your account login to your BungeeBones Member Area and click "Add Funds" in the upper nav bar. You will be presented an invoice that will load your Bitcoin payment safely into cold storage. Your account will be credited and you can then bid for placement as you wish. The positions show their monthly price but those amounts are for reference only. The ad fee will be prorated (by however many days there are in that particular month) and the per-diem fee will be deducted daily from your account.
So in theory you can deposit just one day's worth of Bitcoin and do so every day and your link will be displayed higher everyday. Practically, though, the idea is to let you choose the security of storing as little as possible in your account and balance that with the inconvenience of having to "top off" your account. The balance can also grow daily from ad sales your website makes (if you install the API).
There are other nuances to the bidding such as considering your display rank for your region or location. You don't have to bid to be first at the global level if your customers are all from a specific area.
There is a fully functional demo version of the bidding system too. Just contact the BungeeBones admin with a request for "DemoCoin" and you will be able to try the system for free. The demo version will actually move your link display ahead of all the free links (but not the Bitcoin paying ones).