Jaques seems to be saying that reputation for valor is fleeting. It is something that looks impressive like a large bubble, but it can vanish in an instant like a bursting bubble. Shakespeare expresses a very similar notion in another play, Troilus and Cressida. In that play Achilles has refused to fight because he feels insulted by Agamemnon. Ulysses is trying to persuade Achilles to engage in battle again because he is such a great warrior and so badly needed by the Greeks. Ulysses works on Achilles' pride by getting the other leaders to ignore him and to pretend to be honoring Ajax as their great hero. Ulysses tells Achilles, in effect, that what you have done in the past is quickly forgotten; you have to keep accomplishing new deeds if you want your reputation to remain bright. That is the essence of what Ulysses tells Achilles in a long speech beginning with the following lines.
Time hath, my lord, a wallet at his back,
Wherein he puts alms for oblivion,
A great-siz'd monster of ingratitudes.
Those scraps are good deeds past, which are devour'd
As fast as they are made, forgot as soon
As done. Perseverance, dear my lord,
Keeps honour bright. To have done is to hang
Quite out of fashion, like a rusty mail
In monumental mock'ry. Act III, Scene 3
This is what Jaques is implying when he speaks of the "bubble reputation" in As You Like It. Reputation doesn't last. Therefore, according to Jaques, it isn't worth seeking. He believes that a soldier is foolish to look for something so fragile and valueless at great risk to his own life.
Seeking the bubble reputation
Even in the cannon's mouth. Act II, Scene 7