Home births for dc3 and dc4 here. You will need a more comfortable area and more space than a bath affords to 'comfortably' give birth, unless you have a massive bath!
Home birth 1 was only 2 hours from beginning to end. As dh was starting to lay covers/pillows etc on the floor and I was sat on the sofa my waters broke and within minutes ds was born - on the sofa, never finished laying the protective covers! Midwives put pads down to try and protect the sofa but it was too late after initial waters going and had to replace the sofa. That was an interesting insurance claim!
Home birth 2 was slightly longer - three hours - and we were sorted in time for it happening. (Laid covers out on the floor ready every night before going to bed and put them to the side to grab quickly in the mornings to be more prepared) All mess contained and removed in a big bag for incineration at the hospital. Midwife number two nearly didn't make it in time either! Both births were so quick we wouldn't have had time to get grandparents out of bed and at our house in time to babysit and to then get me to the hospital in time so that was another reason why I was glad we had planned home births.
In our area there was a window of three weeks before your due date to two weeks after where you could have a planned home birth. Any earlier and it was deemed as premature, any later and deemed as overdue, both situations carry greater risks than the on time window so it was hospital birth outside that time. On first date of the window we picked up a big bag of practically everything that might be necessary for the birth, along with two canisters of gas and air. Family doctor prescribed pethidine (I think, can't remember exactly now) in case I wanted it for pain relief, I got it from the pharmacy. We also picked up oxygen with dc3 but midwives brought it in their cars with dc4 in case it was needed and one said that she (along with some other midwives) keeps extra supplies, anything from absorbent pads to nozzles for gas bottles, in her car when she's on call for a home birth in case they are needed.
My midwives knew exactly what they were doing, most even said they prefer home births. They are professional and great at their jobs and the house was cleaner when they left than when they got there! It is worthwhile having a larger area which you are comfortable in for giving birth, you can move around easier too. A bath is restrictive and you won't necessarily be able to get in and out of it in a hurry when 9 months pregnant, it will need a clean out before you use it to have a clean up afterwards, unless you have elsewhere you can use. Also, the sides are high and make things difficult for midwives.