From what you describe, you likely have several possible issues.
As you note, the wireless bridge is 70 Mbps, so assuming the 3560 connection to it is 100 Mbps, what happens to excess bandwidth utilizition? There's a good chance it's dropped on the bridge, where you might not see the drops. This is the likely the smallest bottleneck, but you may have another. (Does the bridge have any stats where it can show drops?)
Since you show 3560Gs on both ends, and mention gig, where gig slows to 100 Mbps you likely have drops. (Are these the drops you're noticing?)
Besides the bottlenecks, i.e. 70 and 100 Mbps vs. gig, what protocol does the SAN device use for its backups? If it uses TCP, TCP, usually by design, detects available bandwidth by ramping up bandwidth utilization until there's drops. I.e., Some drops, for a high bandwidth demanding TCP flow, is quite normal and can't be easily eliminated unless you have a device that can spoof RWIN between devices.
If the SAN device is using some "special" protocol for its backups, difficult to predict how the protocol will work unless the vendor documents it.
With the above background, what might you do?
First, assuming the wireless bridge lacks any effective QoS, we want to keep from sending it more traffic than it can handle. This so we can manage congestion on the 3560s, again assuming it's not possible on the bridge. This could be accomplished to setting the 3560s interfaces connected to the bridge not to exceed 70 Mbps. (E.g. on a 100 Mbps configured interface, "srr-queue bandwidth limit 70". NB: These values are not exact because the hardware adjusts the line rate in increments of six. I.e., you might need to set slower than 70 to insure 70 not exceeded.)
Second, you'll want to configure QoS, such that the backup traffic is identified (hopefully this can be done vs. "normal" SAN traffic). Using two (of the four) egress queues, place all routine traffic in one queue and and backups in another. Use SRR in shared mode and provide the backup queue minimal or little bandwidth and other traffic maximum or most bandwidth. (This will allow backups to use as much as possible available bandwidth, but cause little adverse impact to other traffic.)
With most bandwidth reserved for non-backups, that traffic, assuming there's sufficient bandwidth, should see almost not drops, however backups likely will.
Buffers should be sized for BDP. If they are, there's not much more that can be done on a 3560 to reduce drops for bandwidth probing traffic.
