The thing is the OP has no dcs. If you have dcs then you are more often than not quite stuck. You can't just up sticks when you are lugging a family along.
We have right across the country twice for work post children - know many families who have some who have even emigrated for work with children in tow. Obviously once they get to school age you really try to keep moves down or stay in commutable distance to the school but it's not always possible.
But... the OP is, yes, married, but her dh earns very little money, and they rent. They're not trapped paying a mortgage.I just can't see how moving isn't an option
My first place rent was £600 15 + years ago- it was studio flat and it was on the cheap side for the area.
Up front I needed £900 deposit and £600 rent - so hand to hand over £1500 before I could get keys. First thing I did after every move was try and save up 2500 - 3000 pounds so I had the money for the next move.
Even if OP is in an area with very cheap rents and they find a landlord not asking for much of a deposit - it still going to take money up front that the OP doesn't currently have - just for the flat.
If you don't have it and can't borrow it which in OP circumstances may be impossible rather than just unwise - you don't have it so it's just not an option.
The bike idea could work.
Have a relative who does care work in people's home usually those adverts say you have to have a car - I know I've looked at them - but they knew someone there so got taken on and they bike between locations. DH biked 6 miles back to his digs when he was living away for us - other longer journey he's taken bike on the train for part of journey - though that got bit easier when he got given second hand fold-able bike as a gift.
There are some costs involved with bikes if they are used a lot - plus you have to be able to ride one - I can't due to physical issue - and you have to have access to one. But it can make it affordable to commute further in some cases.
At least Op with no children you don't absolutely have to be back by a certain time - so long unreliable commutes are an option if you can keep costs down by walking or biking.