How do I get proof of my blanket bronze star?

Never heard of a a Bronze Star being issued that way - blanket. Each award for a Bronze Star has its own citation and supporting documentation (Signed DA638 with Orders #). The only "blanket" type awards are unit citations. If I'm wrong - I'm sure an AG type will correct me...but I don't think I am.

The way I understand it, even if it's a "blanket award," there should be a DA Form 638 Awards Recommendation. However, if it does have a completely different process for the "blanket," what you can do is submit a request to the National Archives to receive any and ALL US Military paperwork that has your name on it. If there are orders giving you the Bronze Star, then it should turn up in that search. Or, you can try contacting your old unit and see if they still might have records. Because, it is correct that simple deployment orders sending you to theater and a DD 214 will not be enough. Actual Award Recommendation with signatures and Order Number, or the certificate with an Order Number (both would be better for certain).

The BSM is not a "blanket award". That would require a DA 638 with four achievements and a citation, approved by a general officer.
The CIB and CAB can be awarded with a by-name roster, (this is what is normally referred to as a "blanket award")
Unit awards (PUC, MUC, JMUA) only require your deployment orders showing you were deployed with the right unit during the time frame.
Your DD 214 would list all awards that were complete in your records at the time of separation. Some documents may have reached your record after you separated.
You can access your records here:
https://www.hrcapps.army.mil/portal/
follow the instructions halfway down the right side for creating a DS Login for veterans.