According to the Tewkesbury Chronicle died in 1417 ( recte November 1416) but was not buried until 1420.
This is hard to explain, and may simply be an error. However, given that Constance left no will behind her, there is a good possibility that her death was sudden and unexpected. She was, after all, just over 40, and could easily have expected to live another 20 or even 30 years. She may have died in an accident or from a sudden illness that prevented her from making her will.
Anyway, we have no way of knowing what she intended for the disposal of her body or indeed anything else. Someone would have had to make these decisions for her and her two brothers had both died violently in 1415, meaning that her nearest adult male relative was her son-in-law, Richard Beauchamp, later earl of Worcester. He was only about 21, and due to an arrangement that gave all his paternal inheritance to his mother for life, he had little in the way of resources save for his wife's Despenser inheritance. (Indeed, had it not been for the chance death of her brother in 1413 it is hard to see what this couple would have had to live on - certainly not much.)
Given that Constance was buried in a high-status location near the high altar of Reading Abbey (close to Henry I's tomb) it is probable that she was given a high-status tomb. This would have cost serious money and also some time to fabricate so a delay might be explicable before any ceremony was undertaken. Constance, as a widow, would not have been able to do the usual trick of putting lands in trust to pay for her memorial, so it must have been provided by the young Beauchamps.
I hasten to add that we know nothing of Constance's tomb, as it was destroyed when Reading Abbey was dissolved and no one seems to have recorded it. All that is known is that her great-granddaughter Anne Beauchamp (not to be confused with her aunt, the Kingmaker's wife) was subsequently buried with her.