Cut 2'' thick bamboo butcher block for table top
A router with a template (and template bit or guide collar) is the only way I can think of to get top quality results. An ugly second choice would be a belt sander, but getting your edge to be square to the top and your lines straight will be incredibly hard.

Let's assume you're using a template bit, because the math is easier. Create an exact template out of 1/2" mdf. Rough cut your top to whatever tolerance works with your jigsaw. (I'd suggest 1/4", but if you're getting lots of blade bend, maybe 1/2" is safer.)

Attach the template to the butcher block (hot glue/ doublesided tape/ clamps that you'll have to move around). Take small bites with the router until you're actually being guided by the template. (Note, taking small bites with the router takes practice... work on scrap before you go to town on the real thing.) 

Don't rush, but similarly, don't take too long on the final cut, as there's a high likelihood of burning, which would then have to be sanded out.

Although I love DIY, if you're not extremely comfortable with a router, this is something I'd outsource to an experienced (and tooled-up) woodworker.