Russia and the US are not in a war yet, so there's no necessity for Russia, to have any millitery base near US border, besides, like you said, USA can not allow Russia, to have any millitery base near them, they'll make sure of it. The US clearly has more allies than Russia, and if there's any escalation between the two countries, Russia, will definitely suffer more, they know this fact, and that is probably why their war with Ukraine, is still ongoing, because Ukraine, is an American ally, and it means another strong American base near Russia. America and Russia, have always flexed muscles as far as I can remember, but as it looks today, America, is having an upper hand against Russia.
The military bases I believe, are supposed to be used as a tool to reinforce the power of a country overseas during period of peace, after the war period is done, or at least that is how I have noticed the United States to with their bases all around the world. They won't put a military base in Ukraine and if they wanted to, they lose the chances to reinforce Ukraine when they could... Before the Russian invasion.
Also, even though the United States seems to have more allies internstionally, Russia tries instead to align itself with China and North Korea, which are countries which also happen to hold nuclear weapons, even if they did not, China is one of the biggest military and civilian manufacturers on the planet, so even though it would seem Russia is alone, the Kremlin still has much backing for the years to come, even after all the western brands and investors decided to leave the country.