How do such digital currencies such as Bitcoin affect the independence of Central Banks?
The independence of the central bank means that the bank is independent of the government. A mandate of the central bank is to ensure price stability. However any excess cash the bank prints is the property of the government. The government enjoys having extra income and were it allowed to exercise direct control it may push the bank to print more money. This would undermine the price stability mandate of the bank. Hence in most countries they give the central bank leadership that is independent of the government.
As Bitcoin is not issued by any government that I know of it does not in any way affect this. Perhaps if the government were to bribe the leaders of the bank in Bitcoin...
Bitcoin itself is thought of as a currency. Its an alternative currency to dollars, or pesos or pounds or yen... so its just one more currency. It does not make a big difference for central banks whether its out there or not, unless it becomes so prevalent that people use it more than they do regular currencies. But that's hard. Dollars are more stable in purchasing power in the long run than say Argentinian Pesos, and yet people use the Pesos in Argentina, in part for convenience and in part for legal reasons. So, just because bitcoin might have some advantages does not imply it will take over.
Electronic money issued by central banks instead of paper money issued by central banks has some implications. Potentially has implications of the ability of central bank to expand or contract the money supply on a whim. If money was al digital, all consisting of records a the central banks servers or something like that, the central bank could just multiply everybody's holdings by 1.01 if it wanted money supply to increase by 1%. Easy!