Hello
Yes, it is possible to enter the U.S. on an F-1 visa even if an I-130 is filed and in process. However, you must show that you intend to stay in the U.S. only temporarily and leave at the end of that period. You must also show that you will apply for your green card at the consulate and have an appropriate document ready.
but according to your plans, you want to use the F-1 visa and stay in the US as a student, and if -130 is approved, you want to return to Bulgaria for your I-130 interview ... right? if so, you must know that you are not the only person thinking about it, unfortunately, YOU CAN'T DO THAT . and be in the U.S together and if USCBP is convinced that you are only visiting for a short period of time, you can enter, if not, they can just cancel your F-1 visa and put you back on a plane and send you back to Bulgaria.
a new school with a new I-120 ? dont even think about it. that can let you get deported... YOU CANT STAY IN THE U.S for long time but temporarily. Do you think if you were USCIS you would find that acceptable? I would definitely NOT do that because USCIS and their process doesn't work that way, but at the same time, it's Biden times and the country has no borders so they may not even question you or question but let you in. but I strongly doubt that so prepare yourself and say I'm JUST VISITING .
So Again, it is possible to visit the US, but after passport control it is more likely that you will have a second inspection and then you will have to prove that you are only here for a short time and not meant to be an immigrant -intended immigrant and convince the USCBP , btw, most people think that they have everything when they are married to a US citizen, and they can do what they want. NO ...Their marriage has nothing to do with immigration and is invalid without a process. You can be married to a U.S. citizen and live in your own country or you can be married but never apply for U.S. residency. You can also be married and divorced and as long as you never applied for an immigrant visa, nothing happens.
Good luck