I changed the Linksys AP and the ethernet-bridge to use WEP (10-bits) and found that the performance was like I thought it should be: I have a 2-8mbit (downstream) ADSL connection, and I was seeing downloads in the range of 400-500kbyte/sec with peaks to around 800-900kbyte/sec.
This is the graph:
Problem now is that the laptop has a 3Com 11mbit network card, so I have to buy a 54g card, since it does not connect to the AP when WEP is enabled. It sees the AP, recognizes the signal-strength (excellent!), but it does not connect.