KB versus KB is not a draw unless Bishops are of the same type(light squared or dark squared).
Moreover if bishops are of the same type and players want to continue they are not real Chess players!*** They can't force mate with any probable unskillful play and one can only lose on time or by resigning of the opponent, but even if someone does lose on time, arbiter will still declare the game as a draw as i've have repeatedly have said and do not repeat again.

If someone resigns the game he is in danger of being disqualified from the tournament or face any other penalties if he doesn't provide a sound reason for his resignation.

I'm not an arbiter and in all my career i have never seen anyone resign in a dead position but i believe his resignation will not be accepted and a dead position is an automatic draw even with resignation of one player.


***Chess is not who has the quickest hands. So to play a draw position that no one can win even with the most unskillful play and just try to out-time his opponent is ridiculous.