Or just cut the dowel slightly short and stick a circle of maple veneer on the top (making sure not to get glue on the surface or surrounding veneer).

As you are going the Bigsby route, have you given thought to getting a floating bridge with roller saddles to replace the kit bridge? Say something like this: https://www.amazon.co.uk/dp/B00QA1VJ...&pd_rd_w=kT28H

An unpinned floating bridge is going to be very unstable when using a Bigsby. You could pin a standard floating bridge for more stability, but I'm sure that the use of the Bigsby is still likely to cause the pins to wear away at the wood over time.