Route 251 does not use Broomstick Hall Road.
Sources: 1/3 Facebook posting https://www.facebook.com/groups/684612189032668/posts/2127071114786761/?comment_id=2127109094782963&reply_comment_id=2127131898114016

2/3 Herts CC
https://www.intalink.org.uk/services/fea1c24e-dd65-4033-bad7-d5ba72ed0e36

3/3 BusTimes.org
https://bustimes.org/services/251-upshire-hammond-street#map