diff --git a/Library/Homebrew/dev-cmd/bump-formula-pr.rb b/Library/Homebrew/dev-cmd/bump-formula-pr.rb
index 634fa73110e28b..f0527b046c6dac 100644
--- a/Library/Homebrew/dev-cmd/bump-formula-pr.rb
+++ b/Library/Homebrew/dev-cmd/bump-formula-pr.rb
@@ -324,13 +324,19 @@ def bump_formula_pr
     end
 
     unless args.dry_run?
+      ignore_non_pypi_packages = formula.tap&.pypi_formula_mappings&.key?(formula.full_name).blank?
+      version_or_url_kwargs = if ignore_non_pypi_packages || PyPI.pypi_url?(new_url)
+        { version: new_formula_version.to_s }
+      else
+        { url: new_url }
+      end
       resources_checked = PyPI.update_python_resources! formula,
-                                                        version:                  new_formula_version.to_s,
                                                         package_name:             args.python_package_name,
                                                         extra_packages:           args.python_extra_packages,
                                                         exclude_packages:         args.python_exclude_packages,
                                                         silent:                   args.quiet?,
-                                                        ignore_non_pypi_packages: true
+                                                        ignore_non_pypi_packages: ignore_non_pypi_packages,
+                                                        **version_or_url_kwargs
     end
 
     run_audit(formula, alias_rename, old_contents, args: args)
diff --git a/Library/Homebrew/utils/pypi.rb b/Library/Homebrew/utils/pypi.rb
index 3899bc68bd65f9..f63d4ae6228f81 100644
--- a/Library/Homebrew/utils/pypi.rb
+++ b/Library/Homebrew/utils/pypi.rb
@@ -18,7 +18,7 @@ def initialize(package_string, is_url: false, python_name: "python")
       @pypi_info = nil
       @package_string = package_string
       @is_url = is_url
-      @is_pypi_url = package_string.start_with? PYTHONHOSTED_URL_PREFIX
+      @is_pypi_url = PyPI.pypi_url?(package_string)
       @python_name = python_name
     end
 
@@ -195,6 +195,7 @@ def self.update_pypi_url(url, version)
     params(
       formula:                  Formula,
       version:                  T.nilable(String),
+      url:                      T.nilable(String),
       package_name:             T.nilable(String),
       extra_packages:           T.nilable(T::Array[String]),
       exclude_packages:         T.nilable(T::Array[String]),
@@ -204,7 +205,7 @@ def self.update_pypi_url(url, version)
       ignore_non_pypi_packages: T.nilable(T::Boolean),
     ).returns(T.nilable(T::Boolean))
   }
-  def self.update_python_resources!(formula, version: nil, package_name: nil, extra_packages: nil,
+  def self.update_python_resources!(formula, version: nil, url: nil, package_name: nil, extra_packages: nil,
                                     exclude_packages: nil, print_only: false, silent: false, verbose: false,
                                     ignore_non_pypi_packages: false)
 
@@ -244,11 +245,8 @@ def self.update_python_resources!(formula, version: nil, package_name: nil, extr
       nil
     else
       stable = T.must(formula.stable)
-      url = if stable.specs[:tag].present?
-        url = "git+#{stable.url}@#{stable.specs[:tag]}"
-      else
-        stable.url
-      end
+      url = stable.url if url.blank?
+      url = "git+#{url}@#{stable.specs[:tag]}" if stable.specs[:tag].present?
       Package.new(url, is_url: true, python_name: python_name)
     end
 
@@ -260,8 +258,8 @@ def self.update_python_resources!(formula, version: nil, package_name: nil, extr
       else
         return if ignore_non_pypi_packages
 
-        odie "The main package is not a PyPI package, meaning that version-only updates cannot be \
-          performed. Please update its URL manually."
+        odie "The main package is not a PyPI package, meaning that version-only updates cannot be " \
+             "performed. Please update its URL manually."
       end
     end
 
@@ -403,4 +401,9 @@ def self.pip_report_to_packages(report)
       Package.new "#{name}==#{version}"
     end
   end
+
+  sig { params(url: String).returns(T::Boolean) }
+  def self.pypi_url?(url)
+    url.start_with?(PYTHONHOSTED_URL_PREFIX)
+  end
 end