Thanks for your story, Denis!
We were on La Palma beginning of January this year. At this time, we didn't see any "biking forbidden" signs (or maybe we didn't watch out for them?) and didn't have any encounter with a park ranger. The ranger sitting in the hut at the parking place at Roque Muchachos saw us with our bikes (we were sitting there a rather long time, eating sandwiches for lunch), but didn't bother about us. This seems to be some really abrupt change in policy!
On the trails there were scarcely people, and the few hikers (most of them German) we did encounter, were all really friendly and interested, at the most they were a bit astonished, that one could ride a bike on this terrain. No negative vibrations there.
What a pity, what some supid signs can do to people
On Tenerife it is already the same situation since a few years, as it seems on La Palma now. In 2011 we saw lots of "biking forbidden" signs all over the island of Tenerife, and it was not really fun to bike there, because you always had a bad feeling on the trails. Only the Anaga mountains are still for the most part "free" of those signs. Therefore, in 2013 we only did some Anaga trails on Tenerife, and did not go anywhere else on the island.
As the situation seems now, we will not spend another holiday on La Palma, until they stop this idiocy. I think, bikers are already a quite big economic factor for the tourism industry on La Palma... maybe already bigger than hiking tourism. It will hurt them for sure, if many bikers now turn to other destinations, where they are more welcome. Let's see what happens