The bed trick is admittedly a contrived bit of dramatic foolery, requiring an audience to believe that a woman can, without discovery, go to bed with a man who knows her and expects another. It further requires that an audience credit the woman's willingness to take part in such a deception after being heartlessly cast off by the man years previously. And finally, the existence of a Mariana who can be Isabella's proxy without smirching her own character is itself an unlikely bit of coincidence.
However, coincidence and the failure of a man to recognize his lover were established conventions of Renaissance drama. The deserted wife's return in disguise to her husband was traditional. Shakespeare's audiences were accustomed to accepting in the theater what they would have scoffed at in real life. The modern reader, then, should bear in mind that the bed trick would not have seemed as extraordinary to Shakespeare's original audience as it does now.
Although contrived, it is certainly necessary. In order to bring the play to its final dramatic conclusion, while maintaining Isabella's virtue, Shakespeare had to devise a way to allow her to refuse Angelo's demands while making him think they had been met. Actual compliance would have stained Isabella's purity, damaging her as a symbol of good and destroying the dramatic effect of virtue set against corruption. A flat refusal would have meant that Claudio's execution would go forward unhindered, bringing the play to a conclusion with no opportunity for repentance, forgiveness, and the application of justice with mercy which together form the play's theme.
