When i first visited Shanghai in 1989, there were no bridges or tunnels between the Bund sid eof the river and the Pudong side, only the ferries. (pudong was mostly farms.) The ferries are less used now, but there are still some in operation, incluidng some that run 24 hours a day:
https://en.wikipedia.org/wiki/Shanghai_Ferry
The ferries are especially useful if you want to take a bicycle across the river.