In Amsterdam a bridge over the water connecting Central Amsterdam with the North is always a hot topic, for decades of talking about it sill hasn't materialized. A few serious alternatives that were proposed where tunnels for bikes. But they consistently decide not to do it because of safety concerns at night. Which is hopefully a bigger issue in Amsterdam than Bergen.
I saw something in the news today that the gemeente has earmarked €100m for the bridge, 1/3rd of the total (another 100m coming from another source, and the remaining to be raised.) Bike tunnels under the IJ apparently (so I recall reading, anyway) also have the issue that to have not too steep slopes at the end, the entry/exit points will have to be a reasonable distance from the water itself. https://nltimes.nl/202…
Btw bridge also deal with steepness issues, since they have to be pretty high, and in most cases also have to be able to open.