Our bowler banged it in short of length, in line with the off stump, and the batsman swings across the line sending the ball straight up over the pitch. Both batsmen immediately set off for the run and the wicket keeper stepped in the middle of the pitch to take the catch. The keeper was so bad at the catch attempt that the ball, which had a lot of back spin on it, went straight through his outstretched hands without making any contact whatsoever, and rolled back and hit the stumps all by itself. By this time the runner had reached the batting crease and he just stood there calmly watching the ball come back and hit the stumps. The striker was given out – bowled. Pretty straight forward isn’t it?
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 of
- Run out […]
- 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 already crossed at
the instant of the incident causing the dismissal.
I have left out the parts of the law that apply if there is a runner, as it makes it hard to understand, that is why there are several […] in the quote.