These people are idiots. You can now safely ignore anything else they say about technology forever.
The performance of a video card depends on the graphics chip itself, as well as the memory it is connected to. 64-bit may be bad, or it may be good enough, and while more is typically better, it is not the case always.
With regards to the GT1030 - There are two versions, one uses DDR4 memory, the other GDDR5. You want to avoid the first one like the plague because the card is significantly worse than the one with GDDR5. However, the GT1030 tends to be expensive for what it is, and you can sometimes get an AMD RX460 or RX560 for the same price or cheaper. Those are are also significantly more powerful. A GTX750Ti is a much older card, and while still a decent choice when on a budget, is often as expensive as a faster RX460, especially if you are willing to buy used.
In any case, however, none of the will cause your screen to flicker.
A bit of a longer explanation if you want it: 64-bit vs 128-bit is not solely what is important. The bus width determines how much data can the video card access in a given time period, it is the width of the pipe. However, the second variable is the speed of the flow, or in the case of a video card, the speed of the memory. In other words, if we take 128-bit memory at a given clock speed, and compare it to another set of memory which is 64-bit but clocked twice faster, their effective bandwidth will be the same. This is a simplification, but a decent explanation.