Don't bother buying the stationary bike. It will be wasted money. It's completely possible to recover without ever using one - I did and I know of many others who have done so. In fact, I did no formal exercise at all after my last TKR and my knees bend beautifully.
Your knee can't bend properly because it is swollen. Instead of thinking all the time about doing exercises to help your bend, concentrate much more on reducing the swelling. That's what is preventing your knee from bending. If you think about it, your knee is a bit like a hose that's filled with water - it's stiff and it doesn't bend easily. But get rid of the water and the hose becomes softer and much easier to bend. That's what your knee is like. It's no good doing lots of rest, ice and elevation to reduce swelling, if you keep on doing the exercises that are irritating your knee and making it swell up again.
So, do lots and lots of this:
rest,
elevate,
ice and much, much less exercise. You've been advised several times to cut back the exercising. Please do so.
You see, it's not exercise that brings back your ROM (Range of Motion). It's time, rest, healing and gentle treatment. Your knee isn't lazy or unfit - it's wounded and it needs gentle treatment.
Besides, there's no need to rush to get ROM. Your ROM can continue to improve for a year, or even longer, after a TKR. You've been worried all along about not achieving goals fast enough, but there's no need to worry. Is your PT therapist telling you that you are "behind"? You aren't. You are going at the pace that your knee needs to go.
Myth busting: the "window of opportunity" in TKR
It's all too easy to get into the mind set where you think that the harder you work, the better the results will be. That's often true in life, but it's not true for recovery after a knee replacement.
TKR: work “smarter” and not “harder”
Knee recovery - Lose the Work Ethic!!
Life in the slow lane
What You Should Not Expect To Do After a TKR
Do read these articles and try following the advice. What you've been doing until now hasn't worked very well, so you have nothing to lose by trying something different.