Whats the best advice to progress onto TT bars?
I followed a similar path.  I was road riding then entered into a couple of TT's.  I soon thereafter bought aerobars off of Ebay.  Riding at that angle is different and takes a little getting used to.  I then decided to get a TT bike, but instead of just buying one, I bought a frame and all parts on line, mostly from Ebay, scouring for the best prices on what I wanted that were either slightly used (mostly) or new.  I ended up saving almost $4,000 doing it this way instead of buying a ready to go bike and I learned a lot in the process.  I did have my local bike shop put it all together for around $100.
Good luck.