There should not be a change of strike if the batsman is bowled. The umpire made the correct decision by letting the new batsman face the next ball. This is covered by Law 18, which states that the rule of batsmen crossing only applies if the dismissal is Caught, Obstructing the field or Run out.
11. Batsman returning to original end
(a) When a batsman is dismissed, the not out batsman shall return to his original end [...] with the three exceptions ofRun out [...] Caught Obstructing the field,
for all other methods of dismissal.
Point 12 then goes on to detail what happens in the cases of Caught, Obstructing the field, and Run Out, which is that if the batsmen have crossed, the not out batsman faces the next ball.
12 Batsman returning to wicket he has left
(a) When a batsman is dismissed Caught, Obstructing the field or Run out [...], the not out batsman shall return to the wicket he has left but only if the batsmen had not...