How would I draw a small bridge using pedestrian areas like this?...

I'm guessing this is the Brighton Bandstand at https://www.openstreetmap.org/way/96655710? (Full disclosure -- this building was a little jagged and I just uploaded a changeset to make it into a regular octogon.)

[Answer has been edited to reflect info from the comments below -- thanks @alester @Kovoschiz and @SK53 for the insights!]

For the bridge, I'd probably use a linear highway=footway + bridge=yes + layer=1 without any area tags. I don't think it's necessary to map the exact extent of the bridge, but if I wanted to I'd add a separate polygon tagged with man_made=bridge and layer=1. If this picture is correct, it looks like there are steps leading up to the bridge, so I'd add a short way from the upper promenade to the highway=footway bridge and tag that with highway=steps + incline=up + layer=1. (You might even consider the steps part of the bridge, and if so they'd get the bridge=yes tag as well.)

I'd also use an octagonal linear footway to indicate the walking area around the bandstand, on the cafe roof. Mapping this as an area in addition or instead would also be possible, but I don't feel that it qualifies for highway=pedestrian since it doesn't appear suitable for any kind of emergency or delivery vehicular traffic.

As discussed in the comments below, it's possible to map a 2-D "foot area" as either =footway or =pedestrian, and one might well be more correct than the other in a particular situation, but pedestrian has long had a leg up (heh) because it's a programmed preset in iD.

Furthermore, there's a distinction between omnidirectional highway areas for mapping plazas and other situations where traffic can go anywhere and might enter and exit at a variety of locations, and linear highway areas for adding shape and width details to an already-mapped one-way or two-way linear highway. The omnidirectional areas should get two tags -- highway=* + area=yes -- and the linear areas should be drawn around the existing highway=* way and just be tagged area:highway=*. IMO either of these area methods could be used for the cafe roof, but neither is necessary. The area around the lower cafe level looks like omnidirectional pedestrian to me, and the bridge and upper promenade look like linear ways that could optionally be augmented with a separate area:highway=* way.

Whatever method you ultimately choose, take care that your upper and lower highways don't share any nodes, or routing software might send people jumping off the bandstand level to the cafe below instead of using the steps.