Mussels are a prime source of food for fish in seawater and freshwater -- so it follows that mussels would also be an ideal bait for fishing. If you harvest them yourself, the deal gets even better, since it won't cost you any money. The trick to using mussels as bait is to secure them to the hook; they tend to get pretty slippery.
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Use fresh mussels, not frozen, whenever possible. Fresh mussels are dead too, but they'll give off a fresher smell that may attract more fish. Ideally, you'll have access to an estuary or some other freshwater or seaside location where you can harvest them yourself and use them right away. When you harvest them, follow healthy ecosystem practices and take the larger ones, leaving the smaller ones to grow larger. Also avoid harvesting all the mussels from one area; instead, take them in a random pattern from one area and cover a wider area.
Pry open the shells by sliding a flat butter or blunt knife or a knife specially designed for harvesting mussels into the crack of the shell and pulling the two sides apart.
Slide the flat edge of your knife under the portion of the mussel that is attached to the shell to dislodge it, and then scoop the flesh out carefully.
Slide your bait hook around the thickest part of the mussel, keeping the mussel close to the hook for now. Curve the mussel a bit, and then pierce the flesh a second and third time, if possible, to put as much flesh as possible through the hook. Then, slide the entire mussel up the hook.
Add more mussels to the hook if it's not completely covered. If you're using small mussels, this could be the case.
Tie a knot of cotton string around the top of the hook, and then wind it around the mussel. Tie another knot at the bottom of the hook to hold it in place. Mussels can be loose and sloppy, so this helps to keep them on the hook. You can also use elastic bait thread for this, but biodegradable thread is healthier for the waterways and any creatures that may come into contact with loose thread later on.