I don't know either. The input signal is a very clean sinusoid.
So if I understood correctly there isn't much I can do to see a rectified signal with 1N4148s (uless I work with much higher voltages)?
Schottky BAT54 are only with 3pins? Is there any equivalent with 2 pins?
It is likely that your Function Generator's output BNC shield is grounded to the FG's chassis which in turn is grounded to the mains, and so back through the mains to your scope probe's ground reference lead. So when you connect one scope probe to the output of the bridge in the "usual" manner (probe tip to bridge + and probe ground clip to bridge -) you are in fact creating a groundloop between the AC input from the FG to the output of the bridge. So you are seeing a distorted signal and only one-half of the bridge output. To get around this problem you either need to use an expensive isolated differential voltage probe on the bridge output, OR make a differential measurement of the output using two scope channels, no probe ground connections, and math to subtract, as I showed in the scopetraces I posted on the previous page.
If you want your bridge to work well at 2V input then Schottky diodes are probably necessary. 1n5817 for example.
If you are set on using surface mount BAT54 series diodes you can use one BAT54A and one BAT54C, or two BAT54S, to construct your FWB. These contain two diodes each, in common-anode (A) and common-cathode (C) and series (S) connections. The plain BAT54 (no letter suffix) has three leads also but only contains one diode and the third lead is not connected internally. But they are in tiny SOT-23 packages!