Dear Mr. Bloom,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located the series titled Draft Registration Cards, 1917-1918 in the Records of the Selective Service System (World War I) (Record Group 163) that are in the custody of the National Archives at Atlanta (RE-AT). For access to and/or copies of these records, please contact RE-AT via email at firstname.lastname@example.org.
We suggest that you request a copy of his Official Military Personnel File. Unit information may be listed in his OMPF. OMPFs and individual medical reports for servicemen of the U.S. Army who were separated from the service after October 1912 and prior to 1955 are in the custody of NARA’s National Personnel Records Center in St. Louis. In many cases where personnel records were destroyed in the 1973 fire, proof of service can be provided from other records such as morning reports, payrolls, and military orders, and a certificate of military service will be issued. Please complete a GSA Standard Form 180 and mail it to NARA’s National Personnel Records Center, (Military Personnel Records), 1 Archives Drive, St. Louis, MO 63138-1002.
We searched Ancestry and located All Military Results for Charles Walter Bloom. There may be a fee for using Ancestry to access digitized records. However, you may view these records online at one of NARA's facilities for free via a NARA PC. For the nearest NARA location, please consult our web page at https://www.archives.gov/locations/.
We hope this is helpful. Best of luck with your family research!