What an odd quote, and it's strange that it should end up in Bitesize material (for non-Brits, BBC Bitesize is a resource provided by the BBC to help kids revise for tests) without more precise attribution. It doesn't even explain who Bernard of Clairvaux was, which makes putting in a quote from him even weirder.

At the time this quote claims to be from, Bernard of Clairvaux was busy trying to destroy the reputation of the University of Paris. He was angry that the university was poaching students from monastic schools (including his own) and was trying to get one of the university's most prominent teachers and philosophers - Peter Abelard - tried for heresy. He was successful in this endeavour, securing Abelard's condemnation in 1140 primarily due to his unorthodox views on the Holy Trinity. There were no significant developments in the preaching of crusades in Europe in 1140. The destruction of Edessa, which caused the Second Crusade (which Bernard saw as his pet project), wasn't until 1144.

But the quote definitely sounds like a call to action, which doesn't fit 1140 at all. I am 90% sure the quote is a botched translation of Bernard of Clairvaux's exhortation to join the Second Crusade, which he put in letters sent around various places in Europe in 1146. In the version sent around England, he writes:

But now, O mighty soldiers, men of war, you have a cause for which you can fight without danger to your souls; a cause in which to conquer is glorious and for which to die is gain.

And the version sent around Germany reads:

But now, O brave knight, now, O warlike hero, here is a battle you may fight without danger, where it is glory to conquer and gain to die.

The full letters are online here.

In the letters, this is actually the final rallying cry. In none of these letters is there any mention of Jerusalem and winning a place in heaven. Instead, the letters then move on to issue a note of caution about the treatment of Jews by crusaders and a condemnation of anti-Semitic violence before ending.

The first line of the quote is definitely from Bernard of Clairvaux's crusade summons, but the final sentence is not. Some translators make the questionable decision of offering creative interpretations that capture the spirit of the original Latin text, but not the precise wording. This is why I suspect it is a botched translation. That last sentence about Jerusalem is not in Bernard's letters, but it is the crux of what he was saying. That being said, I have absolutely no idea which translation that is from, and it's possible it was simply whoever the BBC asked to help out with creating this resource - they should've gotten a professional because frankly the whole thing is a bit crap.