It shouldn't be a problem to take the bikes back on most of the major inter-urban bus routes (110, 325, 340, 342, 343, 348, etc). The main thing are size of the doors beneath the bus. There are generally 3 or 4 types, which I'll briefly explain below.
SINGLE BIG DOOR ON EACH SIDE:
The best type has a single big door on either side of the bus... there is obviously no problem taking your bicycles on these type of Titsa buses. Usually you don't need to take off the wheels. Example:
(30+ bikes will fit on the 348 bus service... that bus has the biggest doors of all
TWO OR THREE SMALLER DOORS ON EACH SIDE (with latch handle):
Most often there are buses with smaller cargo doors. In that case, you will need to find the largest compartments. It looks like they won't fit, but trust me with this. Road & mountainbikes WILL fit if you take off both wheels and lower the seatpost. You may also need to remove the pedals if you have a large frame. Put the frame in first with the handlbar tilted 90° towards you. Make sure the cranks are facing outwards. When the frame is tilted at an angle of 45° with respect to the bus, it will fit (just!). Note that downhill bikes will not fit.
Of course if other people have luggage then you may have a problem.
On the bus shown below, you can see two smaller compartments and one larger compartment in the middle. They don't look that much different, but aim for the larger ones!
It might be possible on the smaller forward compartment, but you risk damaging your bicycle.
TWO OR THREE SMALLER DOORS ON EACH SIDE (with no latch handle):
There are also other urban and city buses that have very small doors with no handles - in that case they don't open and the bikes will not be allowed. The classic example is the 345 bus to Aguamansa. It is impossible to fit conventional bicycles on these buses; it's possible
that a folding travel bike will fit:
NO DOORS AT ALL:
Then there are the city buses, commonly seen in and around Santa Cruz. Bikes = impossible!
Images courtesy of: http://www.hidalgoafonso.com
has further information about travelling with bikes on buses in Tenerife (they also have some great MTB trails on their website