1.Bleeding from the base of the tail in a budgie could be due to a broken blood feather.
2.Or may be due to Injury(most likely in this case as per photo shared).
3.Soiling due to loose droppings also looks similar.
4.NOTE- Birds can lose a significant amount of blood quickly, immediate care helps.
Next Steps
A. Clean the Area,,use diluted betadine.
B. If further bleeding, see a vet.
Health Tips
a. Ensure hygiene, cage safety, avoid sharp edges, avoid overcrowding.
b.Balanced diet always helps- Poor nutrition can weaken feathers.
If the problem persists or your budgie seems unwell, you should consult a vet.
Thanks.