Yes, .8cm is within normal limits. The lining typically gets up to 1.6cm thick. Being that you are 48, it's not unusual to have irregular cycles and erratic (heavy and/or prolonged) bleeding since you are likely in perimenopause. There are medications to help regulate it such as (hormonal) contraceptives or non-hormonal tranexamic acid (brand name Lysteda) or even prescription strength NSAID's. Unfortunately, procedures are oftentimes recommended that end up causing more harm than good such as ablation and hysterectomy. You know what they say - sometimes it's best not to mess with mother nature at least in a way that permanently alters our body's natural processes.
Hopefully, your biopsy results will be negative or nothing worse than some mild hyperplasia that can be cured with medication. Let us know what you find out.