There is no element of surprise.
The aircraft are tracked by the Norwegians and the picture is shared. As the cross 30E arounnd the Kola peninsula a penetration time for the UKADR is calculated - working on the assumption they will continue S/SE and penetrate. It is over 2 hours. The QRA takes 1 hour to get there, so there is plenty of time to have a meal, brief, stroll to the jet etc.
Most times they turn back before a scramble, the only tricky ones being when they turn round after reching the Lofoten islands, in which the wheels were normally in the wells as they turned - which meant a quick dump, land and turn.
The normal Bear cruise altitude is around FL360. They normally do not talk to ATC or file a flight plan*. They stay in international airspace over international waters and do not infringe the 12nm limit, so they therefore contravene no laws.
There might be a few eyebrows raised about it, but they pose no military threat. If they wanted to they could launch their ALCMs over the Kola. The general reaction is a general scratching of heads wondering what point Putin is trying to make. It's certainly not one about military might. The Russian armed forces are so emasculated and their population imploding so fast that they are - nukes aside - militarily insignificant.
*Going back to the 80s, the Russians started filing flight plans for their missions in the Norwegian Sea/GIUK gap and then complained if they were intercepted and we broke the standard separation rules.