Nice and easy this one. Park opposite Marlwood School and look for the field gate opposite Quarry Road. From the field gate the Barrow is easily seen. The field had recently been ploughed and as it was raining I didn't fancy getting covered in mud and therefore viewed from the gate. The Barrow was covered in long grass so stood out well against the ploughed brown soil.
This link at South Glos. Council takes you to a leaflet describing a walk round Alveston. It briefly mentions the barrow and suggests that the name derives from 'Alwihs Stone', perhaps a (prehistoric) megalithic stone. Then again, their are historical documents that have another Alveston in Warwickshire once being 'Eanulfeston' (Eanwulf's stone). I think I prefer the (surely not completely stupid) suggestion of 'Elf's stone'. But Alaric Hall's essay (appendix 2) puts paid to that, unfortunately. http://www.alarichall.org.uk/ahphdful.pdf
The fact that the barrow is next to Vattingstone Lane - doesn't that point to a stone as well? It's all very mysterious.