If you're over 65 you can just pay $1.10 on the bus. You don't need a senior Metrocard for this. In principle, you should have some type of identifcation showing your age, e.g. a Medicare card, but in practice this isn't often asked for. If you pay this way you can get a transfer to another bus, but not to the subway.
BTW - Although these are uncommon now, I don't think you can use half dollar coins on the bus. You should be able to use dollar coins, which are also pretty uncommon.
Scroll to the bottom of this URL to get the official rules: