If you go through to
this website you will find various links to auctions in Spain (including one in Tenerife).
With regard to buying directly from banks, I think you really need to be careful - because my experience so far is that you are not getting the rock-bottom price you expect. I was offered some BBVA properties in Santa Cruz as
subastas - but knew the actual building and could tell the prices were higher than the purchase price a few years ago, even though I was assured these were repossessions (in fact, they were not, rather the resale of RIC properties BBVA had invested in for tax breaks five years ago).
On one link from the website above, I followed through Caja España to a 2nd hand property in Palm Mar - Las Olas (still in construction) and the price was more than you could buy it now from the developers' sales office.
I think you will find that it is only those in the know (and with good connections) who manage to pick up the bargains from the banks.