The route called Chaple Gate, from barber booth has been upgraded to a Byway, but currently the Bridleway signs are still up. Also ordnance survey havn't updated their maps yet. If thats the route you mean, then it is legal to use on trail bikes. So is the unclassified road (UCR) along Roych Clough. Im not sure about the bridleway up to edale cross though - that has been a bridleway (and so closed to vehicles) for years.
Because of trail biking (on motorbikes) being such a contentious issue, most riders know what is and what isn't legal, and stick to only legal routes. They do often organise green lane days, where they repair damaged trails and clear flytipping etc. This happened a few weeks back along a legal route near pindale quarry in the Peaks. See http://www.trf.org.uk/ for more info!
Since 2006, the scope for adding new vehiclular rights of way has been limited. However, byway claims put in before 2006 are still valid, and councils are obliged to process these claims in the normal way, due to European laws. There is nothing odd about this, upgrading a bridleway to a byway is just like upgrading a footpath to a bridleway, and can be achieved if 'higher' access rights can be proven through previous use.
With regards to the organisation called gleam, they are effectively 'poo-stirrers'. They have been known to manipulate the law for their own needs, and have also been caught perverting the course of justice with regards to rigging a rights of way case against two trail riders in somerset, fortunately they were caught in the act and the case was dropped! (not that they would tell you this on their website!)
Trail bikes are noisey, and unfortunately the past time attracts alot of people who act like idiots - a lot more than other recreations do! These are its biggest issues IMO and will unfortunately, one day, kill of trail riding in the UK completely. The argment of damage is pretty feeble, its just unfortunate that whatever routes are open to motorcycles are also open to 2000kg 4x4 vehicles. Also the fact that only around 3% of the right of way network is open to vehicles, so the few routes that are open get over used - imagine if non motorised vehicle users were restricted to only 3% of the right of way network, those routes would get trashed too! The general animosity towards motorcyclists in the UK (both on and off road) is unjustified, but its this animosity and 'moral panic' about motorcyclists from the general public that groups like GLEAM and the Ramblers Association feed off when they try to justify banning trail bikes.