See that little jag to the left and back just above the 138 circle? That's a pretty tight corner. If cars are backed up, then they're usually taking it slow, but you might have to get off your bike and carry it around as there is no shoulder at all on the right side of the road going up. You could possibly cross the road, ride on the wrong side of the road, then switch back over after that curve. Then, right where the purple line splits off from the yellow 138 line is a fairly darn steep downhill going down towards Lake Gregory. After a couple hundred yards it mellows out a bit, but there's still not really any shoulder.
Going around the back side of Lake Gregory will have you, after you split off from Lake Dr., going through "residential neighborhoods". They're tight twisty streets that . . . well, there aren't really any streets up in the mountains that have an appreciable bikeway outside the solid white line, so you'll pretty much be in the lane at all times. Once you get over to N. Rd, just before it connects back with highway 189, that's seriously one of the darndest steepest hills up there. When I was young, it used to scare me going zipping down that street in a car, let alone on a bike. Seriously, it's a steep road. In my opinion, the safest road back to the 18 would be Lake Gregory Dr: http://maps.google.com/maps?f=d&hl=e...9823&z=14&om=1
Back when the upper section of the 18 was closed for repairs, traffic was diverted through Crestline via Crest Forest Dr -- this street. It's rather narrow in spots, has some really tight corners, but it's somewhat shorter: http://maps.google.com/maps?f=d&hl=e...UTF8&z=14&om=1
Ignore that little loop on the right, that was a mapping error on my part.
Where in Arrowhead are you going? If you're going to the Village (that shopping center that is at the end of the purple line on your map), I'd reccomend staying on the 18 then going down 173. If you take the 189, the last bit of it from Blue Jay to Lake Arrowhead is one of the twistiest roads on the mountain. Why, it's so twisty that even mountain drivers are forced to slow down to at no more than about 30 miles an hour!
If you're heading counterclockwise around the lake, I'd recomend the Lake Trail from the Village over to this point (it's zoomed in, so zoom out to see the spot I'm mentioning): http://maps.google.com/maps?ie=UTF8&...2494&z=19&om=1
Then it's a short ride to John Muir, which you'd take all the way around to Sunset, to get back to the 173. The 173 from there is pretty much ok (and it's about your only option). If you are going that way, let me know and I'll give you the code for the gate from the Village to the Lake Trail. The Lake Trail does continue from there, but after it rounds the bend (there's a picnic spot there) it starts getting narrow and then the only way off of it is to go up people's stairs past their house. I don't know why, but people sometimes get a little testy when some stranger starts walking up their steps past their house.
If you're interested, let me know what time you'd be likely to be coming along and I can see if anyone I know could possibly pick you up in San Bernardino (or the Crestline Cutoff, if you want to ride up the 18). My email is my username here, @gmail.com