Avidia Bank has spent its nearly century and a half based right around the Assabet Valley, where it keeps its headquarters in Hudson. But now the bank is making a bet on an eastward expansion toward a much more crowded Boston market. The bank borrowed $25 million this summer to finance growth that starts with a new branch in Framingham scheduled to open Sept. 25 at 270 Cochituate Road. "We feel that the opportunities are east of here," said Margaret Melo Sullivan, Avidia's executive vice president, chief financial officer and treasurer. "That's where we feel the opportunities are and where we can grow our business lines."