As Beej said, a plug will hold the screws better than an end grain dowel. I’m not sure where plugs, particularly ones long enough to go through the whole body, can be purchased. If you know someone with a wood lathe they should be able to make some. There’s a reasonable chance the dowels would be fine but if you want the most strength plugs are the way to go. Also, whichever route you go make sure the plug or dowel fits the hole snugly. You shouldn’t have to pound it in but a push fit with maybe a few light taps to get it into place. Titebond isn’t a gap filler. Apologies if you already know that.
Edit: are the bridge screw holes actually going to fall where the string through holes are currently?