One way to do that would be using IRelationRepository.GetParents<NodeEntryRelation> of the product/variant, to get its parent nodes, then use IRelationRepository.GetParents<NodeRelation> recursively (until it returns null) to see if any of its nodes, or grand-nodes matches NodeB

What I did in one of my previous projects, I stored the complete node tree (nodes & sub-nodes) for a product as a property value and also in Episerver Find. Performance-wise its really good.

I created a property with the only getter in my product metaclass. Once the editor publishes a product,  getter automatically create a list of nodes/sub-nodes and store it as the property value. 

The next step is just to check in the code if item-A has NodeB id in the list. 

The property I created was like below 

        public IEnumerable<string> ProductCategories
        {
            get
            {
                string language = "en-GB";
                var _contentLoader = ServiceLocator.Current.GetInstance<IContentRepository>();
                var _linksRepository = ServiceLocator.Current.GetInstance<ILinksRepository>();
                var _referenceConverter = ServiceLocator.Current.GetInstance<ReferenceConverter>();

                var allRelations = _linksRepository.GetRelationsBySource(this.ContentLink);
                var categories = allRelations.OfType<NodeRelation>().ToList();
                List<CatalogContentBase> parentCategories = new List<CatalogContentBase>();
                try
                {
                    if (categories.Any())
                    {
                        foreach (var nodeRelation in categories)
                        {
                            if (nodeRelation.Target != _referenceConverter.GetRootLink())
                            {
                                CatalogContentBase parentCategory =
                                    _contentLoader.Get<CatalogContentBase>(nodeRelation.Target,
                                        new LanguageSelector(language));
                                if (parentCategory != null)
                                {
                                    parentCategories.Add(parentCategory);
                                }
                            }
                        }
                    }
                    else if (this.ParentLink != null && this.ParentLink != _referenceConverter.GetRootLink())
                    {
                        CatalogContentBase parentCategory =
                            _contentLoader.Get<CatalogContentBase>(this.ParentLink,
                                new LanguageSelector(language));
                        parentCategories.Add(parentCategory);
                    }
                }


                catch (Exception ex)
                {
                    // _log.Debug(string.Format("Failed to get categories from product {0}, Code: {1}.", productContent.Name, productContent.ContentLink), ex);
                }
                return parentCategories.Select(x => x.ContentLink.ID.ToString());
            }
        }

That is cool approach but only worth if you need to check a lot. Also there is a problem with that is when you move a content it is not counted as publish. Your better option would be listen to the relation events 

Indeed a cool solution Naveed, but since i don't have to check a lot i think Quan's solution will do the trick.