Well in my opinion the best thing is to leave it alone and hope that it will drain before you need it!
A thought is; dig a trench along the edges, throwing the soil on to the centre of the bed.
What this might do is act like a land drain and excess moisture from the main body of the bed to the sides then in spring throw you papers into the trench to soak up any excess moisture that has flowed to the edges, then back fill the trench.
A picture would have been handy so that we can see what you are trying to achieve,
Whats on my mind is; is the ground on a slope?
If it is; then a trench along the lower edge might suffice!
