Nearest that NX West Midlands gets to Worcestershire border

[Smethwickian]

WMPTE and latterly West Midlands Travel started to run services into Worcestershire just before and then after deregulation day:

X92 (?)

Yes, I remember that - it was the Sunday service put out to tender by the then Hereford & Worcester County Council. At one point I believe WMT added in part of a positioning  journey which ran empty to start in service at Bewdley for Hereford at something like 7am. Will dig out the timetable if I can find it. Never got the chance to try it out during that time but my parents had a day out in Hereford with their WMT  Travelcards.

[Oozells]

NXWM run services into Worcestershire as Frankley is in Worcestershire

(New) Frankley hasn't been in Worcestershire since 1995.

[Crosville]

Stephen,

Get yourself an A-Z atlas of the West Midlands, this shows district and county boundaries as red pecked lines (as does any A-Z atlas). Then you will discover that quite often the boundaries were sensible 100 years ago when they were created but are not nowadays as they cross the middle of housing estates.

No need to, here's a site that has the old historical boundaries, with the modern boundaries, you can impose both, or one or the other
https://www.ordnancesurvey.co.uk/business-and-government/counties/
On this you can see Hall Green & Yardley in Worcestershire, Birmingham City Centre & surrounded by Worcestershire & Staffordshire, Edgbaston cricket ground looks like that's right on the Warwickshire-Worcestershire boundary.