The Protec PB-311 CT case for bari sax is suitable for a low A instrument. It is a hard case, therefore quite hefty, if you put your instrument and some accessories (+ e.g music sheets) in it, the total weight could easily go up to 13-15 kg alltogether.
The body of the instrument fits well in the bag, the neck and one mouthpiece can be stored in a dedicated cushion which is designed to be placed in the instrument's bell (the cushion is part of the package).
There are two additional bags on each side of the case, in one you can store music sheets or other documents of size A4. The bag on the other side is a bit bigger, I was able to put there two additional mouthpieces, several reeds, cleaning stuff and a bottle of water (0.5 L). Filling these pockets can significantly change the balance of the bag, which might be inconvenient if you want to carry it in your hand.
The case's largest dimension is around 112 cm, it might not fit into your car's trunk.
The case can be carried also as a backpack with the separately sold Protec BP-Strap. Due to the weight and size I wouldnt really call it a comfortable outfit and you definitely dont want to carry it like this for kilometers, but for short distances it is ok. Based on my previous experiences this solution is still way better than carrying a case in one hand.