diff --git a/server/src/internalClusterTest/java/org/elasticsearch/action/bulk/BulkProcessor2RetryIT.java b/server/src/internalClusterTest/java/org/elasticsearch/action/bulk/BulkProcessor2RetryIT.java
index 205457b264bb3..caf2b8e73a2fe 100644
--- a/server/src/internalClusterTest/java/org/elasticsearch/action/bulk/BulkProcessor2RetryIT.java
+++ b/server/src/internalClusterTest/java/org/elasticsearch/action/bulk/BulkProcessor2RetryIT.java
@@ -12,6 +12,7 @@
 import org.elasticsearch.action.DocWriteRequest;
 import org.elasticsearch.action.admin.indices.refresh.RefreshRequest;
 import org.elasticsearch.action.search.SearchResponse;
+import org.elasticsearch.client.Client;
 import org.elasticsearch.common.settings.Settings;
 import org.elasticsearch.core.Tuple;
 import org.elasticsearch.index.query.QueryBuilders;
@@ -34,6 +35,12 @@
 public class BulkProcessor2RetryIT extends ESIntegTestCase {
     private static final String INDEX_NAME = "test";
     Map<String, Integer> requestToExecutionCountMap = new ConcurrentHashMap<>();
+    /*
+     * We can't call ESIntegTestCase.client() from a transport thread because it winds up calling a blocking operation that trips an
+     * assertion error if you're doing it from the transport thread. So we stash a random client in this variable for use when we nned a
+     * client in a transport thread.
+     */
+    private Client clientsForTransportThread;
 
     @Override
     protected Settings nodeSettings(int nodeOrdinal, Settings otherSettings) {
@@ -58,7 +65,6 @@ public void testBulkRejectionLoadWithoutBackoff() throws Throwable {
     // value = "org.elasticsearch.action.bulk.Retry2:trace",
     // reason = "Logging information about locks useful for tracking down deadlock"
     // )
-    @AwaitsFix(bugUrl = "https://github.com/elastic/elasticsearch/issues/94941")
     public void testBulkRejectionLoadWithBackoff() throws Throwable {
         boolean rejectedExecutionExpected = false;
         executeBulkRejectionLoad(8, rejectedExecutionExpected);
@@ -66,6 +72,7 @@ public void testBulkRejectionLoadWithBackoff() throws Throwable {
 
     @SuppressWarnings("unchecked")
     private void executeBulkRejectionLoad(int maxRetries, boolean rejectedExecutionExpected) throws Throwable {
+        clientsForTransportThread = client();
         int numberOfAsyncOps = randomIntBetween(600, 700);
         final CountDownLatch latch = new CountDownLatch(numberOfAsyncOps);
         final Set<BulkResponse> successfulResponses = Collections.newSetFromMap(new ConcurrentHashMap<>());
@@ -110,6 +117,8 @@ public void afterBulk(long executionId, BulkRequest request, Exception failure)
                             }
                             rejectedAfterAllRetries = true;
                         }
+                    } else if (failure.getStatus() == RestStatus.SERVICE_UNAVAILABLE) {
+                        // The test framework throws this at us sometimes
                     } else {
                         throw new AssertionError("Unexpected failure status: " + failure.getStatus());
                     }
@@ -128,6 +137,8 @@ public void afterBulk(long executionId, BulkRequest request, Exception failure)
                     rejectedAfterAllRetries = true;
                 }
                 // ignored, we exceeded the write queue size when dispatching the initial bulk request
+            } else if (ExceptionsHelper.status(failureTuple.v2()) == RestStatus.SERVICE_UNAVAILABLE) {
+                // The test framework throws this at us sometimes
             } else {
                 Throwable t = failureTuple.v2();
                 // we're not expecting any other errors
@@ -164,7 +175,7 @@ void countAndBulk(BulkRequest request, ActionListener<BulkResponse> listener) {
         for (DocWriteRequest<?> docWriteRequest : request.requests) {
             requestToExecutionCountMap.compute(docWriteRequest.id(), (key, value) -> value == null ? 1 : value + 1);
         }
-        client().bulk(request, listener);
+        clientsForTransportThread.bulk(request, listener);
     }
 
 }