If you can swing some way to hold the blank in the lathe, then you can get a tailstock 1/2" drill chuck for the tailstock (MT2) for about $7 to hold the bits.
Best way to hold the chuck is either rounded with a collet chuck or a scroll chuck(round or square), but the PSI collet chuck (great chuck at a good price) is probably more like $80. With tax and shipping it would likley be about $100 for both chucks, but then you have an excellent setup. I use this exact setup and would never go back to the drill press. Also the collet chuck has much other usefullness in pen turning.
If you cant swing the collet chuck (or even a scroll chuck), here the cheapesst way. I actually did this before I got my collet chuck, but accuracy will not be there. DOnt use blanks with the setup below that require accurate drilling.
Get a second Harbor freight MT2 chuck, and a bolt to use as a draw bar. You can then use one in each end of the lathe. You will need to turn the blank down to 1/2" on one end to chuck it. I recomend leaving the other end fatter becasue, as I said, accuracy is not there. WIth a 20% off coupon for one of the chucks, you can get this setup for about $15, leaving you some room to buy bits. HF has a bit set up to 1/2 by 64ths for I think under $20 (I use this for all drilling except 7 & 8 MM). This aught to leave you enough of your $50 left to get a couple pen kits, or a metric (7mm maybe) bit.
I hope this helps.
PS. you wont want to stay with the 2 drill chuck setup for any longer than you have to. Sell a couple pens and get the collet chuck as soon as you can. You wont regret it. When you do, you will have 2 tail chucks .. Not a bad thing for convienience