Should I dig up my flower bed and start over?

No need to dig everything out, what I would do though is rake the mulch back, put the compost (Composted cow manure if you can get it) and just rake it into the soil, if you have planted plants, not seeds I would suggest you apply Preen (a weed preventer) to the area to prevent annual weeds, then rake back your mulch. The compost's nutrients will leach into the soil. The plants will need about an inch of water per week, if it doesn't rain, water early morning at the base of the plants. Do not over water, it is the one of the top causes of plant death. Good Luck and Good Gardening!