Is it common for Anglicans to ask a priest to bless their Bibles, wall crosses, and other religious items?
I have oil from the Holy Virgin Cathedral of San Fransisco with which I mark certain items and the doorways of places in which I'm living. Given my general "Reformed" leanings, people get rather surprised to see that I do this.
From your replies, I get the impression that having religious items blessed is an option, but not considered as essential as it is in the Roman Catholic Church.
Yes, it's an option. There's nothing mandatory about it nor is it regarded as essential. Not only is it at the choice of the individual requesting it but there may be some priests who wouldn't do it because they considered it unnecessary.