To avoid the seam bulk, put non-bias strips together with 45 degree instead of straight seam (lay two strip ends face together with one end on right and the other end on top, sew the 45 degree from top left corner to bottom right corner, open & check to ensure will lay smooth, then trim to 1/8" seam allowance). You only need bias binding on a quilt with a curved outside edge. I use 3" strips and fold in half lengthwise with the raw edge next to the quilt front raw edge so it's enclosed in binding.
Always start in the middle of a side and always leave about 10" tail at start so can make 45 degree angle to put two ends together when finish.
To miter corners, stop 1/4" from next edge,backstitch & cut thread; wrap binding around corner of next edge to sort of measure a vertical line on binding, grasp that vertical line and bring up to horizontal edge at corner you are mitering (you now have a fold of fabric brought up to top edge of quilt)pin. Now put the prepared corner back under the pressure foot ready to sew down the next edge and 1/4" from top and right side. Take a couple of stitches, backstitch and keep sewing binding until you reach next corner.
When back to last side, stop about 10" from beginning. You need to have room to fiddle with the two pieces of fabric so you can get that 45degree seam and have the piece fit the quilt. I find if I pin the bindings together to mimick the 45 degree seam, I can check before I sew to ensure I didn't do it backwards. Takes a few minutes, but in the end it is all invisable and no extra bulk.
Flip it over and hand sew the back down with an invisible stitch while you watch tv.
Whew! hope this was clear and wasn't too much info, but since you said you were new to this, thought more was better.