I just started a PhD program in Ancient Judaism straight from undergraduate. I had taken Hebrew, Aramaic, Latin, and German, and I took Ancient Greek the summer before beginning my program. I had applied to 7 schools and only got into one, but I have full funding, and it's a highly regarded program. However, I'd definitely advise going for a masters first. I have to take five classes a semester in order to finish one time, and sometimes I feel like I'm playing a giant game of catch-up.